%!PS-Adobe-3.0 %%Title: (2001-01-23.fm) %%Creator: (FrameMaker+SGML 6.0: AdobePS 8.7.0) %%CreationDate: (12:40 PM Wednesday, January 31, 2001) %%For: (Matt Bishop) %%Routing: (mailto:bishop@cs.ucdavis.edu) %%Pages: 11 %%DocumentFonts: Times-Roman %%+ Times-Bold %%+ Times-Italic %%+ Symbol %%+ Times-BoldItalic %%DocumentNeededResources: font Times-Roman Times-Bold Times-Italic Symbol Times-BoldItalic %%DocumentSuppliedResources: %%DocumentData: Clean7Bit %%PageOrder: Ascend %%Orientation: Portrait %%DocumentMedia: (Default) 612 792 0 () () %RBINumCopies: 1 %RBINupNess: 1 1 %ADO_ImageableArea: 14 12 598 780 %RBIDocumentSuppliedFonts: %%BoundingBox: 0 0 612 792 %%DocumentProcessColors: Cyan Magenta Yellow Black %%DocumentCustomColors: (Red) %%+ (Green) %%+ (Blue) %%+ (PICT Color 1) %%CMYKCustomColor: 0 1 1 0 (Red) %%+ 1 0 1 0 (Green) %%+ 1 1 0 0 (Blue) %%+ 0 0 0 1 (PICT Color 1) %%EndComments %%BeginDefaults %%ViewingOrientation: 1 0 0 1 %%EndDefaults userdict/dscInfo 5 dict dup begin /Title(2001-01-23.fm)def /Creator(FrameMaker+SGML 6.0: AdobePS 8.7.0)def /CreationDate(12:40 PM Wednesday, January 31, 2001)def /For(Matt Bishop)def /Pages 11 def end put %%BeginProlog /md 215 dict def md begin/currentpacking where {pop /sc_oldpacking currentpacking def true setpacking}if %%BeginFile: lw8_feature-1.01 %%Copyright: Copyright 1990-1999 Adobe Systems Incorporated and Apple Computer Incorporated. All Rights Reserved. /bd{bind def}bind def /ld{load def}bd /xs{exch store}bd /Z{0 def}bd /T true def /F false def /level2 /languagelevel where { pop languagelevel 2 ge }{ F }ifelse def /odictstk Z /oopstk Z /fcl { count oopstk sub dup 0 gt { {pop}repeat }{ pop }ifelse countdictstack odictstk sub dup 0 gt { {end}repeat }{ pop }ifelse }bd /sfcl2 { /odictstk countdictstack store count/oopstk xs }bd /efcl2 { stopped{$error/newerror F put}if fcl }bd /noload Z /startnoload { {/noload save store}if }bd /endnoload { {noload restore}if }bd /setcopies{ level2 { 1 dict begin/NumCopies exch def currentdict end setpagedevice }{ userdict/#copies 3 -1 roll put }ifelse }def level2 startnoload /ststpgdev{}def /dopgdev{}def /stpgdev{}def /buf Z /didstop T def /sfcl { /didstop T store /odictstk countdictstack store count/oopstk xs currentfile cvx stopped { $error/newerror F put didstop { save/didstop xs /buf vmstatus exch sub exch pop dup 0 lt{pop 0}if dup 64000 gt{pop 64000}if string store { currentfile buf readline { (}efcl)eq{exit}if }{ /UnexpectedEOF errordict/rangecheck get exec }ifelse }loop didstop restore }if }if fcl }bd /efcl { /didstop F store exec stop }bd level2 endnoload level2 not startnoload /setpagedevice where{pop/realstpgdev/setpagedevice ld}if /SC_topddict Z /SC_spdict Z /$spusrdict F def /dopgdev { userdict/setpagedevice undef $spusrdict { userdict/setpagedevice/realstpgdev load put /$spusrdict F store }if SC_topddict realstpgdev }bd /stpgdev { SC_topddict dup 3 -1 roll { SC_spdict 2 index known { SC_spdict 2 index get dup 3 -1 roll { put dup }forall pop put dup }{ put dup }ifelse }forall pop pop }bd /ststpgdev { /setpagedevice where { userdict eq { /$spusrdict T store }if }if userdict/setpagedevice/stpgdev load put /SC_topddict 0 dict store /SC_spdict 3 dict begin /InputAttributes 0 dict def /Policies 0 dict def /OutputAttributes 0 dict def currentdict end store }def /sfcl/sfcl2 ld /efcl/efcl2 ld level2 not endnoload %%EndFile %%BeginFile: lw8_basic-4.0 /xdf{exch def}bd /:L/lineto /lw/setlinewidth /:M/moveto /rl/rlineto /rm/rmoveto /:C/curveto /:T/translate /:K/closepath /:mf/makefont /gS/gsave /gR/grestore /np/newpath 12{ld}repeat /framewidth -1 def /QDframwid -1 def /numframes Z /mTS matrix def /$m matrix def /av 87 def /por T def /normland F def /psb-nosave{}def /pse-nosave{}def /us Z /psb{/us save store}bd /pse{us restore}bd /level3 /languagelevel where { pop languagelevel 3 ge }{ F }ifelse def level2 startnoload /setjob { statusdict/jobname 3 -1 roll put }bd /devg/DeviceGray def /devr/DeviceRGB def /devc/DeviceCMYK def level2 endnoload level2 not startnoload /setjob { 1 dict begin/JobName xdf currentdict end setuserparams }bd /devg[/DeviceGray]def /devr[/DeviceRGB]def /devc[/DeviceCMYK]def level2 not endnoload /pm Z /mT Z /sD Z /mTSsetup{ mT $m currentmatrix mTS concatmatrix pop }bd /pmSVsetup{ /pm save store }bd /initializepage { mT concat }bd /endp { pm restore }bd /adjRect { dup 2 mul 6 2 roll 4 index sub exch 5 -1 roll sub exch 4 2 roll 4 index add exch 5 -1 roll add exch 4 2 roll }bd /frame1up { gS mTS setmatrix QDframwid lw /setstrokeadjust where{pop T setstrokeadjust}if clippath pathbbox 2 index sub exch 3 index sub exch currentlinewidth framewidth mul adjRect numframes dup 0 lt{pop 0}if { 4 copy rS currentlinewidth framewidth mul 4 mul adjRect }repeat pop pop pop pop gR }bd /$c devr def /rectclip where { pop/rC/rectclip ld }{ /rC { np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K clip np }bd }ifelse /rectfill where { pop/rF/rectfill ld }{ /rF { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl fill gR }bd }ifelse /rectstroke where { pop/rS/rectstroke ld }{ /rS { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K stroke gR }bd }ifelse %%EndFile level3 startnoload %%BeginFile: lw8_safeclipL12-1.0 /rectclip where { pop/rCa/rectclip ld }{ /rCa { np 0 1 index length 4 idiv { 2 copy 4 getinterval aload pop 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K 4 add }repeat clip np pop pop }bd }ifelse /savedstack Z /subsavedstack Z /execstring Z /saferCa { /execstring xs /odictstk countdictstack store /oopstk 0 store count 0 ne { savedstack 0 eq{ count 100 gt{count}{100}ifelse array/savedstack xs }{ count savedstack length gt { count array/savedstack xs }if }ifelse count savedstack 0 3 -1 roll getinterval astore/subsavedstack xs }{ /subsavedstack 0 store }ifelse execstring cvx stopped { $error/newerror F put newpath }if fcl subsavedstack 0 ne{ subsavedstack aload pop }if }bd %%EndFile level3 endnoload level3 not startnoload %%BeginFile: lw8_safeclipL3-1.0 /saferCa/pop ld %%EndFile level3 not endnoload %%BeginFile: lw8_level1_colorspace-2.0 /G/setgray ld /:F1/setgray ld /:F/setrgbcolor ld /:F4/setcmykcolor where { pop /setcmykcolor ld }{ { 3 { dup 3 -1 roll add dup 1 gt{pop 1}if 1 exch sub 4 1 roll }repeat pop setrgbcolor }bd }ifelse /:Fx { counttomark {0{G}0{:F}{:F4}} exch get exec pop }bd /$cs Z /:rg{devr :ss}bd /:sc{$cs :ss}bd /:dc { dup type/arraytype eq{0 get}if dup/DeviceCMYK eq { pop devc 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F def /ps Z level2 startnoload /pushcolor/currentrgbcolor ld /popcolor/setrgbcolor ld /setcmykcolor where { pop/currentcmykcolor where { pop/pushcolor/currentcmykcolor ld /popcolor/setcmykcolor ld }if }if level2 endnoload level2 not startnoload /pushcolor { currentcolorspace $c eq { currentcolor currentcolorspace T }{ currentcmykcolor F }ifelse }bd /popcolor { { setcolorspace setcolor }{ setcmykcolor }ifelse }bd level2 not endnoload /pushstatic { 2state? $o $t $p $s $cs ps }bd /popstatic { /ps xs /$cs xs /$s xs /$p xs /$t xs /$o xs /2state? xs }bd /pushgstate { currentpoint pushcolor currentlinewidth currentlinecap currentlinejoin currentdash exch aload length np clippath pathbbox $m currentmatrix aload pop }bd /popgstate { $m astore setmatrix 2 index sub exch 3 index sub exch rC array astore exch setdash setlinejoin setlinecap lw popcolor np :M }bd /bu { errordict/nocurrentpoint{pop 0 0}put 2state? { pushgstate gR }if pushgstate gR pushgstate pushstatic pm restore mTS setmatrix }bd 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}forall }bd /$ckeyd md def /:skey { 1 index maxlength 2 index length sub ge { begin /$mkeys 20 dict def /$mkeys load end dup/$ckeyd xs }if 3 1 roll put }bd /fD1pass { 40 $ckeyd //md ne { pop 1 }if $ckeyd exch :skey }bd /:searchdict Z /:searchdict { exch 2 copy known { get }{ exch/$mkeys get :searchdict }ifelse }bd /lU { //md exch 2 copy known { get }{ exch /$mkeys get :searchdict }ifelse }bd /:xs{ exch 0 1 2 index length 1 sub{ 3 copy gS 1 getinterval show gR exch get 0.0 rm }for pop pop }bd /:ys{ exch 0 1 2 index length 1 sub{ 3 copy gS 1 getinterval show gR exch get 0.0 exch rm }for pop pop }bd /:xys{ exch 0 1 2 index length 1 sub{ 3 copy gS 1 getinterval show gR exch 2 mul 2 copy 1 add get 3 -2 roll get exch rm }for pop pop }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd /fD1pass/def ld /lU/load ld level2{ /:xs/xshow ld /:ys/yshow ld /:xys/xyshow ld }if level2 not endnoload /:xbl{ currentpoint 2 index exec :M .03 ps mul currentpoint 2 index 0.0 rm 3 index exec :M currentpoint 2 index dup rm 3 index exec :M 0.0 1 index rm exch exec neg 0.0 exch rm }bd /:xot{ currentpoint -2.0 0.0 rm 2 index exec :M currentpoint 0.0 -2.0 rm 2 index exec :M currentpoint 0.0 2.0 rm 2 index exec :M currentpoint 2.0 0.0 rm 2 index exec :M gS gl exec currentpoint gR :M }bd /:xsh{ 2 ps 0.05 mul add 2 copy currentpoint 5 2 roll 0.0 rm exec currentpoint 6 2 roll sub moveto :xot moveto }bd /fD Z /sf Z /scf Z /sf1pass { lU setfont }bd /scf1pass { exch lU exch scalefont fD }bd /scf2pass { scalefont fD }bd md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff fD }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff fD }bd /ps Z /fz{/ps xs}bd /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse fD }def %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin /fD/def ld/sf/setfont ld /scf/scf2pass ld %RBIIncludeNonPPDFeature: NumCopies 1 %RBIBeginNonPPDFeature: WaitTimeout 600 600/languagelevel where{pop languagelevel 2 ge}{false}ifelse{1 dict dup/WaitTimeout 4 -1 roll put setuserparams}{statusdict/waittimeout 3 -1 roll put}ifelse %RBIEndNonPPDFeature sfcl{ %%BeginFeature: *InputSlot Upper %%EndFeature }efcl sfcl{ %%BeginFeature: *ManualFeed False level2 {1 dict dup /ManualFeed false put setpagedevice}{statusdict begin /manualfeed false store end} ifelse %%EndFeature }efcl sfcl{ %%BeginFeature: *PageRegion Letter level2 { 2 dict dup /PageSize [612 792] put dup /ImagingBBox null put setpagedevice }{ /letter where {pop letter}{letterR} ifelse } ifelse %%EndFeature }efcl (Matt Bishop)setjob /mT[1 0 0 -1 14 780]def %RBIIncludeStartNup /sD 16 dict def %%IncludeResource: font Times-Roman /f133/Times-Roman :mre /f148 f133 10 scf 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All rights reserved. %%BeginProcSet: "FrameMacDict" 556 12 userdict/FrameMacDict 250 dict put FrameMacDict begin systemdict/setpacking known{/fMSP currentpacking def true setpacking}if[/fM1/fMi1/fMi2/fM2/fM3/fMcl /fMAB/fM5/fM6/fM0/fM8/fM9/fMBC/fMC/fMCD/fMCK/fMCR/fMCS/fMib/fMCN/fMCE/fMCO/fMef /fMet/fMeh/fMew/fMey/fMex/fMei/fMej/fMek/fMel/fMeb/fMGC/fMGL/fMGM/fMIT/fMIx /fMJB/fMJC/fMJG/fMJK/fMJM/fMJR/fMJY/fMK/fML1/fMM/fMCP/fMNC/fMNg/fMND/fMOx/fMPC /fMPG/fMPH/fMPt/fMRC/fMS/fMSJ/fMUC/fMUM/fMUY/fMY/fMdm/fMax/fMa2/fMi/fMk/fMSD /fMcu/fMsg/fms/fMTV/fmBS/fMdp/freq/sangle/sflipx/sflipy/pflipx/pflipy/xx/yy /xindex/yindex/fM1B/fM0B/fMdc/fMds]{0 def}forall/T true def/F false def/FmBD{ bind def}bind def/fmXD{exch def}FmBD/fmBx{dup length exch{dup/FrameMacDict eq{ pop FrameMacDict}{dup type dup/arraytype eq exch/packedarraytype eq or{dup xcheck{fmBi}if}if}ifelse exch}forall systemdict/setpacking known{packedarray}{ array astore}ifelse cvx}FmBD/fmBi{bind fmBx}FmBD/fmax{2 copy lt{exch}if pop} FmBD/fmin{2 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def/fm_s /show load def/fm_a/ashow load def/fm_w/widthshow load def/fm_y/awidthshow load def/RealKshow/kshow load def/fm_si systemdict/image get def/fm_sg systemdict /setgray get def/fm_sc systemdict/currentgray get def/fm_su systemdict /settransfer get def/fm_sx systemdict/currenttransfer get def fMCE{ /SysColorimage systemdict/colorimage get def}if/fMdm matrix def/fMax matrix def /fMa2 matrix def/fmSM{fMax currentmatrix pop}FmBD/fmRM{fMax setmatrix}FmBD/FmRF {currentpoint 2 copy translate 4 2 roll{-1 1 scale}if rotate neg exch neg exch translate}FmBD/FmU4 true def systemdict/pdfmark known systemdict /currentdistillerparams known and{/fMAB true def/FmPD/pdfmark load def/FmPT /fm_s load def currentdistillerparams/CoreDistVersion get 2000 ge{/FmPD2 /pdfmark load def currentdistillerparams/CoreDistVersion get 4050 ge{/FmPD4 /pdfmark load def}{/FmPD4{FmU4{ (%%[Acrobat Distiller 4.05 and up is required to generate Logical PDF Structure]%%) =(%%[Logical PDF Structure is not generated.]%%)= flush}if/FmU4 false def cleartomark}FmBD}ifelse/fmCG true def/FmND{mark exch/Dest exch 5 3 roll/View[ /XYZ 5 -2 roll FmDC null]/DEST FmPD}FmBD/FmPA{fmCG{pop pop pop}{FmND}ifelse} FmBD}{/FmPD4/cleartomark load def/FmPD2/cleartomark load def/FmPA{pop pop pop} FmBD/FmND{pop pop pop}FmBD}ifelse}{/fMAB false def/FmPD/cleartomark load def /FmPD2/cleartomark load def/FmPD4/cleartomark load def/FmPT/pop load def/FmPA{ pop pop pop}FmBD/FmND{pop pop pop}FmBD}ifelse/FmDC{transform fMdm defaultmatrix itransform cvi exch cvi exch}FmBD/FmBx{dup 3 index lt{3 1 roll exch}if 1 index 4 index lt{4 -1 roll 3 1 roll exch 4 1 roll}if}FmBD/fmkn{2 copy known{get T}{ pop pop false}ifelse}FmBD/fmfp{exch currentfont dup/FontMatrix get exch /FontInfo fmkn{T}{currentfont/df fmkn{dup/FontInfo fmkn{3 1 roll/FontMatrix get mtx concatmatrix exch T}{pop pop pop F}ifelse}{pop pop F}ifelse}ifelse{3 -1 roll fmkn{exch 0 3 1 roll dtransform neg exch pop exch pop}{pop exec}ifelse}{ exec}ifelse}FmBD/FmTx{/fM3 fmXD/fM2 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eq exch fMCP eq or{{{1 exch sub}currenttransfer fmcp fm_su}if}{pop fmSW}ifelse}ifelse/fMIT fmXD/fM5 fmXD /fM8 fmXD/fM6 fmXD/fMrw fmXD/fMcl fmXD translate rotate scale{-1 1 scale}if fMIT 1 ne{{1 exch sub fMIT mul 1 exch sub}currenttransfer exch fmcp fm_su}if /fMi1 fM8 string def fMcl fMrw fM6[fMcl 0 0 fMrw fMcl 2 div fMrw 2 div]{ currentfile fMi1 fM5{readstring}{readhexstring}ifelse pop}fM9{{fMi1}{fMi1}T 3 SysColorimage}{fm_si}ifelse fM7 restore}FmBD}{/Fmi{save userdict/fM7 3 -1 roll put/fM9 F def{{dup length dup 1 sub/fMGL fmXD array/fMGC fmXD/fMBC fmXD/fMNC fmXD/fMRC fmXD fMeb fMCP ne{fmSC[/Indexed/DeviceGray fMGL{fMGC exch get}] setcolorspace}{[/Indexed/DeviceRGB fMGL{dup fMRC exch get exch dup fMNC exch get exch fMBC exch get}]setcolorspace}ifelse}{dup length 1 sub/fMGL fmXD/fMGC fmXD[/Indexed/DeviceGray fMGL{fMGC exch get}]setcolorspace fMeb dup fMK ne exch fMCP ne and{fmSW}if}ifelse}{1 5 index bitshift 1 sub/fMGL fmXD[/Indexed /DeviceGray fMGL 5 -1 roll{{fMGL div 1 exch sub}}{{fMGL div}}ifelse] setcolorspace fMeb dup fMK ne exch fMCP ne and{fmSW}if}ifelse/fMIT fmXD/fM5 fmXD/fM8 fmXD/fM6 fmXD/fMrw fmXD/fMcl fmXD translate rotate scale{-1 1 scale}if fMIT 1 ne{{1 exch sub fMIT mul 1 exch sub}currenttransfer exch fmcp fm_su}if /fMi1 fM8 string def 7 dict begin/ImageType 1 def/Width fMcl def/Height fMrw def/ImageMatrix[fMcl 0 0 fMrw fMcl 2 div fMrw 2 div]def/DataSource{currentfile fMi1 fM5{readstring}{readhexstring}ifelse pop}def/BitsPerComponent fM6 def /Decode[0 fMGL]def currentdict end fm_si fM7 restore}FmBD}ifelse/fmIv{[{1 exch sub}/exec load dup currenttransfer exch]cvx bind fm_su}FmBD/fm3b{dup fMCP eq{ pop 0 1 4 index length 1 sub{3 index 1 index get .3 mul 3 index 2 index get .59 mul 3 index 3 index get .11 mul add add round cvi 4 index 3 1 roll put}for pop pop}{/fmRY fmGG 0 1 6 index length 1 sub{5 index 1 index get 255 div 5 index 2 index get 255 div 5 index 3 index get 255 div 4 index exec 6 index fMC eq{pop pop pop}{6 index fMM eq{pop pop exch pop}{6 index fMY eq{pop 3 1 roll pop pop}{ 6 index fMK eq{4 1 roll pop pop pop}{pop pop pop pop 0}ifelse}ifelse}ifelse} ifelse 255 mul round cvi 6 index 3 1 roll put}for pop pop pop pop}ifelse}FmBD /Fmci{save userdict/fM7 3 -1 roll put/fMIT fmXD/fM5 fmXD/fM8 fmXD/fM6 fmXD/fMrw fmXD/fMcl fmXD/fMi1 fM8 string def/fM0 fM8 3 idiv def/fMs fMi1 0 fM0 getinterval def/fMs2 fMi1 fM0 dup getinterval def/fMs3 fMi1 fM0 dup 2 mul exch getinterval def translate rotate scale{-1 1 scale}if fMIT 1 ne{{1 exch sub fMIT mul 1 exch sub}currenttransfer exch fmcp fm_su}if fMcl fMrw fM6[fMcl 0 0 fMrw fMcl 2 div fMrw 2 div]fMeb fMCP eq fMCE and{{currentfile fMi1 fM5{readstring}{ readhexstring}ifelse pop pop fMs}{fMs2}{fMs3}T 3 SysColorimage}{{fmIv currentfile fMi1 fM5{readstring}{readhexstring}ifelse pop pop fMs fMs2 fMs3 fMeb fm3b}fm_si}ifelse fM7 restore}FmBD/fm4b{dup fMCP eq{pop 0 1 5 index length 1 sub{2 copy get dup 6 index 3 index get add 255 fmin .3 mul 1 index 6 index 4 index get add 255 fmin .59 mul 3 -1 roll 5 index 4 index get add 255 fmin .11 mul add add round cvi 5 index 3 1 roll put}for pop pop pop}{dup fMC eq{pop pop pop pop}{dup fMM eq{pop pop pop exch pop}{dup fMY eq{pop pop exch pop exch pop} {fMK eq{4 1 roll pop pop pop}{pop pop pop 0 1 2 index length 1 sub{1 index exch 0 put}for}ifelse}ifelse}ifelse}ifelse}ifelse}FmBD/Fmc4{save userdict/fM7 3 -1 roll put/fMIT fmXD/fM5 fmXD/fM8 fmXD/fM6 fmXD/fMrw fmXD/fMcl fmXD/fMi1 fM8 string def/fM0 fM8 4 idiv def/fMs fMi1 0 fM0 getinterval def/fMs2 fMi1 fM0 dup getinterval def/fMs3 fMi1 fM0 dup 2 mul exch getinterval def/fMs4 fMi1 fM0 dup 3 mul exch getinterval def translate rotate scale{-1 1 scale}if fMIT 1 ne{{1 exch sub fMIT mul 1 exch sub}currenttransfer exch fmcp fm_su}if fMcl fMrw fM6[ fMcl 0 0 fMrw fMcl 2 div fMrw 2 div]fMeb fMCP eq fMCE and{{currentfile fMi1 fM5 {readstring}{readhexstring}ifelse pop pop fMs}{fMs2}{fMs3}{fMs4}T 4 SysColorimage}{fmIv{currentfile fMi1 fM5{readstring}{readhexstring}ifelse pop pop fMs fMs2 fMs3 fMs4 fMeb fm4b}fm_si}ifelse fM7 restore}FmBD fML1{/fmAn{ transform round .5 sub exch round .5 sub exch itransform}FmBD/fmAc{transform round 1.5 sub exch round 1.5 sub exch itransform}FmBD/fmDn{dtransform round exch round exch idtransform}FmBD/fmLn{0 dtransform exch cvi 2 idiv 2 mul .1 add exch idtransform pop}FmBD/FmCv{fmDn 6 2 roll fmDn 6 2 roll fmDn 6 2 roll rcurveto}FmBD}{T setstrokeadjust/fmAn{}FmBD/fmAc{}FmBD/fmDn{}FmBD/fmLn{}FmBD /FmCv{rcurveto}FmBD}ifelse/FmM{fmAn moveto}FmBD/M{moveto}FmBD/N{0 rmoveto}FmBD /S{fm_s}FmBD/A{0 exch fm_a}FmBD/W{0 exch 32 exch fm_w}FmBD/X{0 exch 0 32 5 2 roll fm_y}FmBD/fmQP{fML1 fMGM or not{FmG dup 1 fm_g exec FmR}if exec}FmBD/FmB{ newpath fmAn moveto}FmBD/FmL{rlineto}FmBD/FmAL{fmAn lineto}FmBD/FmSo{fmLn setlinewidth setlinecap{fm_t}fmQP 0 0 moveto}FmBD/FmS{fmLn setlinewidth closepath{fm_t}fmQP 0 0 moveto}FmBD/FmDS{fmLn setlinewidth setlinecap{closepath }if setdash{fm_t}fmQP[]0 setdash 0 0 moveto}FmBD/FmFl{FmG{fm_e}fmQP FmR}FmBD /fmq{fmDn 4 2 roll fmAn newpath moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}FmBD/FmqP{fmq fmLn setlinewidth{fm_t}fmQP 0 0 moveto}FmBD /FmqF{fmq FmG{fm_f}fmQP FmR}FmBD/FmKp{{currentpoint}stopped{F 5 1 roll}{T 7 3 roll}ifelse fmDn 4 2 roll fmAn newpath moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath clip{moveto}{newpath}ifelse}FmBD/FmKb{{currentpoint} stopped}FmBD/FmKe{clip{newpath}{moveto}ifelse}FmBD/FmAF{FmG newpath fmAn translate not{0.0 0.0 moveto}if rotate fmDn scale 0.0 0.0 1.0 5 3 roll arc closepath{fm_f}fmQP FmR}FmBD/FmAP{FmG{setdash}if fmLn setlinewidth setlinecap fmSM newpath 2 index 2 div add exch 3 index 2 div sub exch fmAn 2 index 2 div sub exch 3 index 2 div add exch translate rotate scale 0.0 0.0 1.0 5 3 roll exch arcn{closepath}if fmRM{fm_t}fmQP FmR}FmBD/FmST{FmG fmAn translate .3 fmLn setlinewidth 0 setlinecap 0 setlinejoin newpath 1 fm_g 0 0 10 0 360 arc fm_f 0 fm_g 0 0 10 0 360 arc fm_t 36{1 0 moveto 0 0 10 -2.5 2.5 arc fm_f 10 rotate} repeat FmR}FmBD/FmSL{FmG fmAn translate .25 fmLn setlinewidth 0 setlinecap 0 setlinejoin newpath 1 fm_g 0 0 10 0 360 arc fm_f 0 fm_g 10 .5 fmLn neg .1{0 0 3 -1 roll 0 360 arc fm_t}for FmR}FmBD/fMCP 0 def/fMC 1 def/fMM 2 def/fMY 3 def /fMK 4 def/fMS 5 def/fMN 6 def/fMNg 0 currenttransfer exec .5 gt def/fMib fMCP def/fMJK 0 def/fMJY 0 def/fMJM 0 def/fMJC 0 def/fMJR 1 def/fMJG 1 def/fMJB 1 def/fMPG 0 def/fMTV 1 def/fMPt null def/fMCK[0 0 0 1(Black)0 0 0]def/fmCH{fML1{ 14 dict dup begin fMCE{/HalftoneType 2 def currentcolorscreen[/GraySpotFunction /GrayAngle/GrayFrequency/BlueSpotFunction/BlueAngle/BlueFrequency /GreenSpotFunction/GreenAngle/GreenFrequency/RedSpotFunction/RedAngle /RedFrequency]{exch def}forall}{/HalftoneType 1 def currentscreen[/SpotFunction /Angle/Frequency]{exch def}forall}ifelse statusdict/checkscreen known{ statusdict/accuratescreens get exec}{F}ifelse/AccurateScreens exch def end}{ currenthalftone}ifelse}FmBD/fmSH{fML1 fMeb fMCP ne or{begin statusdict /checkscreen known{currentdict/AccurateScreens known{AccurateScreens}{F}ifelse statusdict/setaccuratescreens get exec}if HalftoneType 1 eq{Frequency Angle /SpotFunction load setscreen}{HalftoneType 2 eq{fMeb fMCP eq fMCE and{ RedFrequency RedAngle/RedSpotFunction load GreenFrequency GreenAngle /GreenSpotFunction load BlueFrequency BlueAngle/BlueSpotFunction load GrayFrequency GrayAngle/GraySpotFunction load setcolorscreen}{fMeb fMC eq{ RedFrequency RedAngle/RedSpotFunction load}{fMeb fMM eq{GreenFrequency GreenAngle/GreenSpotFunction load}{fMeb fMY eq{BlueFrequency BlueAngle /BlueSpotFunction load}{fMeb fMY eq currentdict/BlackFrequency known and{ BlackFrequency BlackAngle/BlackSpotFunction load}{GrayFrequency GrayAngle /GraySpotFunction load}ifelse}ifelse}ifelse}ifelse setscreen}ifelse}if}ifelse end}{sethalftone}ifelse}FmBD/FmCS{17 dict begin/HalftoneType 2 def /AccurateScreens exch def/GraySpotFunction exch def/GrayAngle exch def /GrayFrequency exch def/BlackSpotFunction exch def/BlackAngle exch def /BlackFrequency exch def/BlueSpotFunction exch def/BlueAngle exch def /BlueFrequency exch def/GreenSpotFunction exch def/GreenAngle exch def /GreenFrequency exch def/RedSpotFunction exch def/RedAngle exch def /RedFrequency exch def currentdict dup end/fMPH exch def fmSH}FmBD/FmSS{5 dict begin/HalftoneType 1 def/AccurateScreens exch def/SpotFunction exch def/Angle exch def/Frequency exch def currentdict dup end/fMPH exch def fmSH}FmBD/fMPH fmCH def/fmcp{cvlit exch cvlit exch 2 copy length exch length add array dup 0 4 index putinterval dup 3 index length 3 index putinterval 3 1 roll pop pop cvx} FmBD/fmEp{sub dup 0 lt{neg}if .001 le}FmBD/fmQC{2 copy 0 get exch 0 get fmEp{2 copy 1 get exch 1 get fmEp{2 copy 2 get exch 2 get fmEp{3 get exch 3 get fmEp}{ pop pop F}ifelse}{pop pop F}ifelse}{pop pop F}ifelse}FmBD/fmQR{2 copy 5 get exch 0 get fmEp{2 copy 6 get exch 1 get fmEp{7 get exch 2 get fmEp}{pop pop F} ifelse}{pop pop F}ifelse}FmBD/FmSC{/fMib fMS def/fMJB fmXD/fMJG fmXD/fMJR fmXD /fMCN fmXD/fMJK fmXD/fMJY fmXD/fMJM fmXD/fMJC fmXD}FmBD/FmSP{/fMib fmXD fmGb fmCC}FmBD/fMSC 1 dict def/FrameSetSpotColors{dict FrameMacDict/fMSC 3 -1 roll put}fmBi def/FrameSpot{FrameMacDict/fMSC get exch dup 4 get exch put}fmBi def /fMGM T def/fm4q{4{4 index eq 8 1 roll}repeat pop pop pop pop and and and}FmBD /fmGb{/fMeb fMCP def/fMcu/setcustomcolor where{pop T}{F}ifelse def/fMsg /setseparationgray where{pop T}{F}ifelse def/setcmykcolor where{/fMSD T def /setcmykcolor get dup/fm_x fmXD/fmSK fmXD}{/fMSD F def/fmSK{4 1 roll 3{3 index add 0 fmax 1 fmin 1 exch sub 3 1 roll}repeat fm_r pop}FmBD}ifelse fMSD{fMcu{0 fm_sx exec 1 fm_sx exec eq{/fMeb fMN store}{/fm_x where{pop 1 0 0 0 fm_x fm_sc 0 1 0 0 fm_x fm_sc 0 0 1 0 fm_x fm_sc 0 0 0 1 fm_x fm_sc 4{4 copy}repeat 0 1 1 1 fm4q{/fMeb fMC store}if 1 0 1 1 fm4q{/fMeb fMM store}if 1 1 0 1 fm4q{/fMeb fMY store}if 1 1 1 0 fm4q{/fMeb fMK store}if 1 1 1 1 fm4q{/fMeb fMN store}if}if }ifelse}if}if}FmBD/fmCC{/fMND F def/fMCT fMTV 1 fMPG sub mul def fMib fMCP eq{ fMGM fML1 or not{fMeb fMCP eq{fMAB not{[/Pattern[/DeviceCMYK]]setcolorspace fMCK 0 4 getinterval aload pop fMCT 1 lt{4{fMCT mul 4 1 roll}repeat}if}{[ /Pattern[/DeviceRGB]]setcolorspace fMCK 5 3 getinterval aload pop fMCT 1 lt{3{1 exch sub fMCT mul 1 exch sub 3 1 roll}repeat}if}ifelse}{fMcu fMCS and{fMCK 0 5 getinterval aload pop findcmykcustomcolor fMCT setcustomcolor}{0 1 3{fMCK exch get fMCT mul}for fm_x}ifelse currentgray[/Pattern[/DeviceGray]]setcolorspace} ifelse fMPt setcolor}{fMsg fMCR and{1 fMCT sub setseparationgray}{fMcu fMCS and {fMCK 0 5 getinterval aload pop findcmykcustomcolor fMCT setcustomcolor}{fMAB not fMSD and{0 1 3{fMCK exch get fMCT mul}for fm_x}{5 1 7{fMCK exch get 1 exch sub fMCT mul 1 exch sub}for fm_r}ifelse}ifelse}ifelse}ifelse}{fMGM fML1 or not{ [/Pattern[/DeviceGray]]setcolorspace 1 fMCT sub fMPt setcolor}{1 fMCT sub fm_g} ifelse}ifelse}FmBD/K{fMCK astore pop/fMCS T def/fMCR F def/fMTV exch def fmCC} FmBD/H{0 0 0 1(Black)0 0 0 fMCK astore pop/fMCS F def/fMCR T def/fMTV exch def fmCC}FmBD/fMCS F def/fMCR F def/fmPK{fMCK astore pop/fMCS F def/fMCR F def/fMTV exch def fmCC}FmBD/FmCC{1 0 0 0(Cyan)0 1 1 fmPK}FmBD/FmCM{0 1 0 0(Magenta)1 0 1 fmPK}FmBD/FmCY{0 0 1 0(Yellow)1 1 0 fmPK}FmBD/FmCK{0 0 0 1(Black)0 0 0 fmPK} FmBD/G{FmCK}FmBD/B{1 G}FmBD/FmOP/setoverprint where{pop/setoverprint}{/pop} ifelse load def fML1{/patScreenDict 7 dict dup begin<0f1e3c78f0e1c387>[45{pop}{ exch pop}.5 2 sqrt]FmBD<0f87c3e1f0783c1e>[135{pop}{exch pop}.5 2 sqrt]FmBD[0{pop}dup .5 2]FmBD[90{pop}dup .5 2]FmBD<814224 1818244281>[45{2 copy lt{exch}if pop}dup .75 2 sqrt]FmBD<0102040810204080>[45{ pop}{exch pop}.875 2 sqrt]FmBD<8040201008040201>[135{pop}{exch pop}.875 2 sqrt] FmBD end def}{/fMPP 5 dict dup begin<0f87c3e1f0783c1e>{3 setlinewidth -1 -1 moveto 9 9 lineto fm_t 4 -4 moveto 12 4 lineto fm_t -4 4 moveto 4 12 lineto fm_t}FmBD<0f1e3c78f0e1c387>{3 setlinewidth -1 9 moveto 9 -1 lineto fm_t -4 4 moveto 4 -4 lineto fm_t 4 12 moveto 12 4 lineto fm_t}FmBD<8142241818244281>{1 setlinewidth -1 9 moveto 9 -1 lineto fm_t -1 -1 moveto 9 9 lineto fm_t}FmBD<80 40201008040201>{1 setlinewidth -1 -1 moveto 9 9 lineto fm_t 4 -4 moveto 12 4 lineto fm_t -4 4 moveto 4 12 lineto fm_t}FmBD<0102040810204080>{1 setlinewidth -1 9 moveto 9 -1 lineto fm_t -4 4 moveto 4 -4 lineto fm_t 4 12 moveto 12 4 lineto fm_t}FmBD end def/fMPD 15 dict dup begin/PatternType 1 def/PaintType 2 def/TilingType 3 def/BBox[0 0 8 8]def/XStep 8 def/YStep 8 def/PaintProc{begin fMPP fmBS known{fMPP fmBS get exec}{8 8 T[1 0 0 -1 0 8]fmBS fm_m}ifelse end} FmBD end def}ifelse/fMdp 72 0 fMdm defaultmatrix dtransform dup mul exch dup mul add sqrt def/freq fMdp dup 72 div round dup 0 eq{pop 1}if 8 mul div def /sangle 1 0 fMdm defaultmatrix dtransform exch atan def sangle fMa2 rotate fMdm defaultmatrix fMa2 concatmatrix dup 0 get/sflipx exch def 3 get/sflipy exch def fML1{/fmgF{fMa2 exch get mul 0 lt{-1}{1}ifelse}FmBD}if/fmPM fML1{{dup patScreenDict exch known{patScreenDict exch get aload pop freq mul 5 2 roll fMa2 currentmatrix 1 get 0 ne{3 -1 roll 90 add 3 1 roll sflipx 1 fmgF sflipy 2 fmgF mul}{sflipx 0 fmgF sflipy 3 fmgF neg mul}ifelse 0 lt{exch pop}{pop}ifelse fMNg{{neg}fmcp}if bind systemdict/setscreen get exec}{/fmBS fmXD/fM1B 0 def /fM0B 0 def freq 0 fMa2 currentmatrix 1 get 0 ne{90 add/pflipx sflipx 1 fmgF def/pflipy sflipy 2 fmgF def}{/pflipx sflipx 0 fmgF def/pflipy sflipy 3 fmgF neg def}ifelse{pflipy mul/yy fmXD pflipx mul/xx fmXD/xindex xx 1 add 2 div 8 mul cvi def/yindex yy 1 add 2 div 8 mul cvi def fmBS yindex xindex 8 idiv add get 1 7 xindex 8 mod sub bitshift and 0 ne fMNg{not}if{/fM1B fM1B 1 add def 1}{ /fM0B fM0B 1 add def 0}ifelse}setscreen fM0B fM0B fM1B add div fMNg{1.0 exch sub}if}ifelse/fMPG exch def/fMGM F def fmCC}}{/fMPC 8 dict def{dup fMPC exch known{fMPC exch get}{dup fMPD/fmBS 3 -1 roll put fMPD matrix makepattern dup fMPC 4 -1 roll 3 -1 roll put}ifelse/fMPt exch def/fMPG 0 def/fMGM F def fmCC}} ifelse FmBD/fmgr{fMGM not{/fMGM T def fML1{fMPH fmSH}if}if/fMPG exch def fmCC} FmBD/FmP{FrameFillPatternsArray exch get dup type/stringtype eq{fmPM}{fmgr} ifelse}FmBD/fMEd 40 dict def/fmPE{fMEd 3 1 roll fmBi put}bind def/fmgS 32 array def/fMgt 0 def/fMtp 0 def/fmSG{fmgS fMgt get dup null eq{pop fmgS fMgt 10 dict dup 4 1 roll put}if 3 1 roll put}FmBD/fmGG{fMgt -1 -1{fmgS exch get dup null ne {2 copy exch known{2 copy exch get/_notdef ne{exch get dup exit}if}if}if pop} for pop}FmBD/gsave{FrameMacDict begin FmG/fMgt fMgt 1 add def fmgS fMgt get dup null eq{pop}{dup dup{pop/_notdef put dup}forall pop pop}ifelse end}fmPE /grestore{FrameMacDict begin fMgt fMtp gt{/fMgt fMgt 1 sub def}if FmR null fmCN end}fmPE/grestoreall{FrameMacDict begin/fMgt fMtp def fm_l null fmCN end}fmPE /save{FrameMacDict/fm_v get exec FrameMacDict begin/fMgt fMgt 1 add def fmgS fMgt get dup null eq{pop}{dup dup{pop/_notdef put dup}forall pop pop}ifelse /fMtp fMgt def end}fmPE/fMND F def/fMCC null fmSG/fMOP F fmSG/fMKO F fmSG/fmRY{ 1 exch sub 3 1 roll 1 exch sub 3 1 roll 1 exch sub 3 1 roll 3 copy 2 copy le{ pop}{exch pop}ifelse 2 copy le{pop}{exch pop}ifelse dup dup dup 6 1 roll 4 1 roll 7 1 roll sub 6 1 roll sub 5 1 roll sub 4 1 roll}fmSG userdict/fM7 known not{userdict/FrameSuccessfull F put userdict/FrameEndPictStopped F put userdict /fM7 0 put}if/fmLC{fMSC{exch pop exch dup 3 -1 roll fmQC{pop T exit}if}forall dup T ne{pop F}if}FmBD/fmLR{fMSC{exch pop exch dup 3 -1 roll fmQR{pop T exit}if }forall dup T ne{pop F}if}FmBD/fmLM{fMSC exch known}FmBD/fmCN{fMND F fMib fMCP ne{/fMOP fmGG{/fMKO fmGG{pop T}if}if}if dup/fMND exch def{pop pop}{exch dup null ne{exch pop dup type dup/integertype eq exch/realtype eq or{fm_g}{setcolor }ifelse}{pop{1 fm_g}if}ifelse}ifelse}FmBD/findcmykcustomcolor{0 0 0 8 array astore}fmPE/findrgbcustomcolor{FrameMacDict begin 4 1 roll 3 copy/fmRY fmGG exec 8 4 roll 8 array astore end}fmPE/findgraycustomcolor{0 0 0 exch 1 exch sub exch findcmykcustomcolor}fmPE/findhsbcustomcolor{FrameMacDict begin 4 1 roll gsave fm_h currentrgbcolor grestore 4 -1 roll findrgbcustomcolor end}fmPE /setcustomcolor{FrameMacDict begin dup type dup/integertype eq exch/realtype eq or not{1.0}if exch dup/fMCC exch fmSG dup 4 get dup fmLM{fMib fMS eq{fMCN eq{ pop}{pop pop 0}ifelse}{pop pop pop 0}ifelse}{pop fMib fMK eq{3 get mul}{fMib fMY eq{2 get mul}{fMib fMM eq{1 get mul}{fMib fMC eq{0 get mul}{pop pop 0} ifelse}ifelse}ifelse}ifelse}ifelse dup 0 le/fMKO exch fmSG 1 exch sub fmCN end} fmPE/setoverprint{FrameMacDict begin dup FmOP/fMOP exch fmSG null fmCN end}fmPE /currentoverprint{FrameMacDict begin/fMOP fmGG end}fmPE/setrgbtocmyk{ FrameMacDict begin/fmRY exch fmSG null fmCN end}fmPE/currentrgbtocmyk{ FrameMacDict begin/fmRY fmGG end}fmPE/fill{FrameMacDict begin fMND{newpath}{ fm_f}ifelse end}fmPE/eofill{FrameMacDict begin fMND{newpath}{fm_e}ifelse end} fmPE/stroke{FrameMacDict begin fMND{newpath}{fm_t}ifelse end}fmPE/fmNX{load fMND{FmG fMa2 currentmatrix end nulldevice setmatrix exec currentpoint FrameMacDict/FmR get exec moveto}{end exec}ifelse}fmBi def/show{FrameMacDict begin/fm_s fmNX}fmPE/ashow{FrameMacDict begin/fm_a fmNX}fmPE/widthshow{ FrameMacDict begin/fm_w fmNX}fmPE/awidthshow{FrameMacDict begin/fm_y fmNX}fmPE /kshow{FrameMacDict begin/RealKshow fmNX}fmPE/image{FrameMacDict begin dup type /dicttype ne{fMib fMK eq{/fm_i load end exec}{FmG fmSW/fm_i load end exec FrameMacDict begin FmR end}ifelse}{fML1{(image)errordict/typecheck get exec}{ dup begin ImageType 1 eq{currentcolorspace 0 get dup/DeviceGray eq{pop Decode 0 get 0 eq Decode 1 get 1 eq and{pop Width Height BitsPerComponent ImageMatrix /DataSource load fMEd/image get end end exec}{end/fm_i load end exec}ifelse}{ dup/DeviceRGB eq exch/DeviceCMYK eq or{T 0 2 Decode length 2 sub{Decode exch get 0 eq and}for 1 2 Decode length{Decode exch get 1 eq and}for{pop Width Height BitsPerComponent ImageMatrix/DataSource load currentdict /MultipleDataSources known{MultipleDataSources}{F}ifelse{aload pop T}{F}ifelse Decode length 2 idiv fMEd/colorimage get end end exec}{end/fm_i load end exec} ifelse}{end/fm_i load end exec}ifelse}ifelse}{end/fm_i load end exec}ifelse} ifelse}ifelse}fmPE/separationimage{fm_i}fmPE %% The definition of the /imagemask (up to version @@/main/28) used to simulate the definition %% of /image. The structure of the code was the same, and both executed `nulldevice' for non-black %% plates. (/image executed `nulldevice' via `fmSW' call). %% This appears to be incorrect, because of the difference between `image' and `imagemask' %% operators. While `image' operator always paints with black color, which is why the %% definition of /image dicriminated between black and other colors plates, `imagemask' %% operator paints with the current color. Therefore, the discrimination between black and %% other colors plates in /imagemask definition, with sending non-black plates to `nulldevice' %% seems to be wrong, and is eliminated in this version. %% %% itenenbo, cahaverl 07/02/98 %% /imagemask{FrameMacDict begin dup type/dicttype ne{/fm_m load end exec}{/fm_m load end exec}ifelse}fmPE/separationimagemask{fm_m}fmPE/colorimage{FrameMacDict begin FmG dup 4 eq{fmIv pop{/fMP4 exch def/fMP3 exch def/fMP2 exch def/fMP1 exch def{fMP1 fMP2 fMP3 fMP4 fMib fm4b}fm_si}{/fMP1 exch def 1 index 8 ne{ (colorimage)errordict/rangecheck get exec}if/fMs 4 index string def/fMs2 4 index string def/fMs3 4 index string def/fMs4 4 index string def{fMP1 0 1 fMs length 1 sub{2 copy 4 mul 4 getinterval forall fMs4 5 index 3 -1 roll put fMs3 4 index 3 -1 roll put fMs2 3 index 3 -1 roll put fMs 3 -1 roll put}for pop fMs fMs2 fMs3 fMs4 fMib fm4b}fm_si}ifelse}{dup 3 eq{fmIv pop{/fMP3 exch def/fMP2 exch def/fMP1 exch def{fMP1 fMP2 fMP3 fMib fm3b}fm_si}{/fMP1 exch def 1 index 8 ne{(colorimage)errordict/rangecheck get exec}if/fMs 4 index string def/fMs2 4 index string def/fMs3 4 index string def{fMP1 0 1 fMs length 1 sub{2 copy 3 mul 3 getinterval forall fMs4 4 index 3 -1 roll put fMs3 3 index 3 -1 roll put fMs 3 -1 roll put}for pop fMs fMs2 fMs3 fMib fm3b}fm_si}ifelse}{1 eq{pop image}{ (colorimage)errordict/rangecheck get exec}ifelse}ifelse}ifelse FmR end}fmPE /customcolorimage{FrameMacDict begin FmG setcustomcolor currentgray 0 gt{ currentgray 1 ge{/fMOP fmGG{nulldevice}{fMNg{{pop 0}}{{pop 1}}ifelse fm_su} ifelse}{[1 currentgray sub/mul cvx]cvx currentransfer fmcp fm_su}ifelse}if/fm_i get end exec FrameMacDict begin FmR end}fmPE/setgray{FrameMacDict begin fMib fMK eq{F}{fMib fMS eq fMJR 0 eq and fMJG 0 eq and fMJB 0 eq and{F}{pop 1 T} ifelse}ifelse/fMKO exch fmSG fmCN end}fmPE/setseparationgray{FrameMacDict begin /fMKO F fmSG null fmCN fm_sg end}fmPE/setrgbcolor{FrameMacDict begin 3 copy[4 1 roll]fmLR{fMib fMS eq{fMJB eq exch fMJG eq and exch fMJR eq and{0 F}{1 T}ifelse }{pop pop pop 1 T}ifelse}{/fmRY fmGG exec fMib fMK eq{1.0 exch sub 4 1 roll pop pop pop F}{fMib fMY eq{pop 1.0 exch sub 3 1 roll pop pop F}{fMib fMM eq{pop pop 1.0 exch sub exch pop F}{fMib fMC eq{pop pop pop 1.0 exch sub F}{pop pop pop pop 1 T}ifelse}ifelse}ifelse}ifelse}ifelse/fMKO exch fmSG fmCN end}fmPE /sethsbcolor{FrameMacDict begin fm_h currentrgbcolor setrgbcolor end}fmPE /currentcmykcolor where{pop}{/currentcmykcolor{FrameMacDict begin currentrgbcolor/fmRY fmGG exec end}fmPE}ifelse/setcmykcolor{FrameMacDict begin fMib fMK eq{1.0 exch sub 4 1 roll pop pop pop dup 1.0 ge}{fMib fMY eq{pop 1.0 exch sub 3 1 roll pop pop dup 1.0 ge}{fMib fMM eq{pop pop 1.0 exch sub exch pop dup 1.0 ge}{fMib fMC eq{pop pop pop 1.0 exch sub dup 1.0 ge}{pop pop pop pop 1 T}ifelse}ifelse}ifelse}ifelse/fMKO exch fmSG fmCN end}fmPE/setcmykoverprint{ FrameMacDict begin 4 copy[5 1 roll]fmLC{fMib fMS eq{0 fmax fMJK eq exch 0 fmax fMJY eq and exch 0 fmax fMJM eq and exch 0 fmax fMJC eq and{0 F}{1 T}ifelse}{ pop pop pop pop 1 T}ifelse}{fMib fMK eq{1.0 exch sub 4 1 roll pop pop pop dup 1 fmin exch 1 gt}{fMib fMY eq{pop 1.0 exch sub 3 1 roll pop pop dup 1 fmin exch 1 gt}{fMib fMM eq{pop pop 1.0 exch sub exch pop dup 1 fmin exch 1 gt}{fMib fMC eq {pop pop pop 1.0 exch sub dup 1 fmin exch 1 gt}{pop pop pop pop 1 T}ifelse} ifelse}ifelse}ifelse}ifelse/fMKO exch fmSG fmCN end}fmPE/setcmykcoloroverprint{ setcmykoverprint}fmPE/setcmybcolor{setcmykcolor}fmPE/FrameEr where{pop}{ userdict/FrameEr(\000)put}ifelse/fMSJ 100 string def/fmXC{FmE countdictstack userdict begin/showpage{}def/FrameDictStackDepth exch def count/FrameStackDepth exch def userdict/EndFrame5NestedPS dup FrameMacDict exch get put userdict /FrameSuccessfull false put FrameMacDict/fMHq get/$brkpage where dup{exch pop} if or{userdict/FrameEndPictStopped false put}{userdict/FrameEndPictStopped true put currentfile cvx stopped pop FrameSuccessfull not{systemdict/clear get exec userdict/FrameEr get 0 1 put FrameMacDict begin FmG systemdict/initmatrix get exec 0 systemdict/setgray get exec clippath{pathbbox}stopped{100 100 512 692}if exch pop add 2. div newpath moveto(Courier-BoldOblique)findfont 18 scalefont setfont FrameEr1 fm_s( \()fm_s $error begin errorname 20 string cvs fm_s(, ) fm_s/command load 128 string cvs fm_s end(\))fm_s FrameEr2 print flush FrameMacDict/fMSJ get{dup currentfile exch{readline}stopped{pop exch pop T}if not{exit}if(EndFrame5NestedPS)eq{exit}if}loop grestore end}if userdict /FrameSuccessfull false put userdict/FrameEndPictStopped false put FrameMacDict /fmIR get exec}ifelse}fmBi def/FmEp{save userdict/fM7 3 -1 roll put exch fMeb fMCP eq fMib fMCP ne and and{fMEd{userdict 3 1 roll put}forall}if FmOP[/fMef /fMet/fMeh/fMew/fMey/fMex/fMei/fMej/fMek/fMel]{fmXD}forall fMex fMey translate fMet rotate fMew fMeh scale fMef{-1 1 scale}if 1 fMej fMel sub div 1 fMek fMei sub div scale fMej fMel add 2 div neg fMei fMek add 2 div neg translate 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit[]0 setdash newpath fML1 not{F setstrokeadjust}if fmXC}FmBD/FmPI{0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit[]0 setdash newpath newpath 0 0 moveto}FmBD/FmPc{save userdict/fM7 3 -1 roll put newpath 3 index neg 3 index neg translate 1 -1 scale 0.0 0.0 moveto fmXC}FmBD/fmIR{end countdictstack FrameDictStackDepth sub dup 0 gt{{end}repeat}{pop}ifelse count FrameStackDepth sub dup 0 gt{{pop}repeat}{pop}ifelse fM7 restore FrameMacDict begin}fmBi def /EndFrame5NestedPS{userdict/FrameEndPictStopped get{userdict/FrameSuccessfull true put stop}{FrameMacDict/fmIR get exec}ifelse}fmBi def/alphaimage where{pop} {userdict/alphaimage{1 ne{limitcheck}if not{limitcheck}if pop image}put}ifelse /fmDE{systemdict/initgraphics get exec clippath{pathbbox}stopped{100 100 512 692}if exch pop add 2. div newpath moveto(Courier-BoldOblique)findfont 18 scalefont setfont currentpoint 2 copy FrameEr3 fm_s 20 sub 2 copy moveto FrameEr4 fm_s 20 sub 2 copy moveto(\()fm_s statusdict/jobname get fm_s(\))fm_s 20 sub moveto FrameEr5 fm_s showpage}FmBD/cd where{dup/cd get/fmRC fmXD/cd{ FrameMacDict begin FrameEr 0 get 0 ne{fmDE}if/fmRC load end exec}fmBi put}{ /endp where{dup/endp get/fMRE fmXD/endp{FrameMacDict dup dup/FmU4 get exch/fMRE get exec/FmU4 exch put FrameEr 0 get 0 ne{FrameMacDict begin currentfile fMSJ{ readline}stopped{pop exch pop true}if pop dup(%%Trailer)eq{pop fmDE}{cvx exec} ifelse end}if}fmBi put}if}ifelse systemdict/setpacking known{fMSP setpacking}if end %%EndProcSet /md where{pop countdictstack array dictstack true exch{md eq{pop false exit}if} forall{md begin}if}if %FRMSetup FrameMacDict begin /FrameEr1(PostScript error)def /FrameEr2(A PostScript error occurred. FrameMaker+SGML is attempting recovery.)def /FrameEr3(FrameMaker+SGML has detected one or more)def /FrameEr4(PostScript errors in this document.)def /FrameEr5(Please check your output.)def /FrameFillPatternsArray [ 0 0.1 0.3 0.5 0.7 0.9 0.97 1 <0F1E3C78F0E1C387> <0F87C3E1F0783C1E> <8142241818244281> <0102040810204080> <8040201008040201> ] def end %%EndSetup %%Page: 1 1 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 1 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 0 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 0 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 0 0 :M f148 sf ( )S 2 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Outline for January 23, 2001)S 70.709 N (ECS 251 \320 Winter 2001)S 159.015 N (Page )S (1)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 3 0 :M f175 sf ( )S 7 0 :M FrMacBegin B 0 FmP F FmOP 181.612 72 M (Outline f)S -0.453 N (or J)S -0.272 N (anuary 23, 2001)S FmE 7 0 :M f148 sf ( )S 9 0 :M FrMacBegin B 0 FmP F FmOP 58 102.667 M (1.)S 10.5 N (Greetings and felicitations!)S 76 114.667 M (a.)S 11.062 N (No class on January 25 or January 30; no of)S -0.251 N (\336)S (ce hours on )S -0.3 N (W)S -0.801 N (ednesday)S -0.652 N (, January 24 or Monday)S -0.652 N (, January 29)S 76 126.667 M (b)S -0.4 N (.)S 10.9 N (Extra of)S -0.251 N (\336)S (ce hour: Friday January 26: 11 )S -0.552 N (AM\3201 PM)S 58 138.667 M (2.)S 10.5 N (Distrib)S -0.2 N (uted system?)S 76 150.667 M (a.)S 11.062 N (What is it?)S 76 162.667 M (b)S -0.4 N (.)S 10.9 N (Wh)S -0.051 N (y use it?)S 58 174.667 M (3.)S 10.5 N (System )S -0.552 N (Architectures)S 76 186.667 M (a.)S 11.062 N (minicomputer mode)S 76 198.667 M (b)S -0.4 N (.)S 10.9 N (w)S -0.1 N (orkstation model)S 76 210.667 M (c.)S 11.062 N (processor pool)S 58 222.667 M (4.)S 10.5 N (Issues)S 76 234.666 M (a.)S 11.062 N (global kno)S -0.251 N (wledge)S 76 246.666 M (b)S -0.4 N (.)S 10.9 N (naming)S 76 258.666 M (c.)S 11.062 N (scalability)S 76 270.666 M (d.)S 10.5 N (compatibility)S 76 282.666 M (e.)S 11.062 N (process synchronization, communication)S 76 294.666 M (f.)S 12.172 N (security)S 76 306.666 M (g.)S 10.5 N (structure)S 58 318.666 M (5.)S 10.5 N (Netw)S -0.1 N (orks)S 76 330.666 M (a.)S 11.062 N (goals)S 76 342.666 M (b)S -0.4 N (.)S 10.9 N (message, pack)S -0.1 N (et, subnet, session)S 76 354.666 M (c.)S 11.062 N (switching: circuit, store-and-forw)S -0.1 N (ard, message, pack)S -0.1 N (et, virtual circuit, dynamic routing)S 76 366.666 M (d.)S 10.5 N (OSI model: PDUs, layering)S 94 378.666 M (i.)S 12.722 N (ph)S -0.051 N (ysical: ethernet, aloha, )S FmE 10 0 :M f203 sf ( )S 12 0 :M FrMacBegin B 0 FmP F FmOP 214.405 378.666 M (etc)S FmE 12 0 :M f148 sf ( )S 14 0 :M FrMacBegin B 0 FmP F FmOP 226.06 378.666 M (.)S 94 390.666 M (ii.)S 9.943 N (data link layer: frames, parity checks, link encryption)S 94 402.666 M (iii.)S 7.165 N (netw)S -0.1 N (ork layer: virtual circult vs. datagram, routing via \337)S (ooding, static routes, dynamic routes, central-)S 112 414.666 M (ized routing vs. distrib)S -0.2 N (uted routing; congestion solutions \(pack)S -0.1 N (et discarding, isarithmic, chok)S -0.1 N (e pack)S -0.1 N (ets\))S 94 426.666 M (i)S -0.251 N (v)S -0.652 N (.)S 8.625 N -0.018(transport: services pro)W -0.151 N -0.018(vided \(UDP vs. )W -0.181 N -0.018(TCP\), functions to higher layers, addressing schemes \(\337)W -0.018(at, DNS, )W 112 438.666 M (etc.\), g)S -0.051 N (ate)S -0.251 N (w)S -0.1 N (ay fragmentation and reassembly)S 94 450.666 M (v)S -0.652 N (.)S 11.152 N (session: adds session characteristics lik)S -0.1 N (e authentication)S 94 462.666 M (vi.)S 7.722 N (presentation: compression, end-to-end encryption, virtual terminal)S 94 474.666 M (vii.)S 4.943 N (application: user)S -0.2 N (-le)S -0.251 N (v)S -0.151 N (el programs)S 58 486.666 M (6.)S 10.5 N (Clocks)S 76 498.666 M (a.)S 11.062 N (happened-before relation)S 76 510.666 M (b)S -0.4 N (.)S 10.9 N (Lamport\325)S -0.552 N (s distrib)S -0.2 N (uted clocks: )S FmE 15 0 :M f203 sf ( )S 17 0 :M FrMacBegin B 0 FmP F FmOP 213.487 510.666 M (a)S FmE 17 0 :M f148 sf ( )S 19 0 :M FrMacBegin B 0 FmP F FmOP 218.487 510.666 M ( )S FmE 20 0 :M f237 sf ( )S 22 0 :M FrMacBegin B 0 FmP F FmOP 220.987 510.666 M (\256)S FmE 22 0 :M f148 sf ( )S 24 0 :M FrMacBegin B 0 FmP F FmOP 230.855 510.666 M ( )S FmE 25 0 :M f203 sf ( )S 27 0 :M FrMacBegin B 0 FmP F FmOP 233.355 510.666 M (b)S FmE 27 0 :M f148 sf ( )S 29 0 :M FrMacBegin B 0 FmP F FmOP 238.355 510.666 M ( means )S FmE 30 0 :M f203 sf ( )S 32 0 :M FrMacBegin B 0 FmP F FmOP 268.9 510.666 M (C)S FmE 32 0 :M f148 sf ( )S 34 0 :M FrMacBegin B 0 FmP F FmOP 275.57 510.666 M (\()S FmE 35 0 :M f203 sf ( )S 37 0 :M FrMacBegin B 0 FmP F FmOP 278.897 510.666 M (a)S FmE 37 0 :M f148 sf ( )S 39 0 :M FrMacBegin B 0 FmP F FmOP 283.897 510.666 M (\) < )S FmE 40 0 :M f203 sf ( )S 42 0 :M FrMacBegin B 0 FmP F FmOP 297.865 510.666 M (C)S FmE 42 0 :M f148 sf ( )S 44 0 :M FrMacBegin B 0 FmP F FmOP 304.535 510.666 M (\()S FmE 45 0 :M f203 sf ( )S 47 0 :M FrMacBegin B 0 FmP F FmOP 307.862 510.666 M (b)S FmE 47 0 :M f148 sf ( )S 49 0 :M FrMacBegin B 0 FmP F FmOP 312.862 510.666 M (\))S 76 522.666 M (c.)S 11.062 N (Example where )S FmE 50 0 :M f203 sf ( )S 52 0 :M FrMacBegin B 0 FmP F FmOP 158.966 522.666 M (C)S FmE 52 0 :M f148 sf ( )S 54 0 :M FrMacBegin B 0 FmP F FmOP 165.636 522.666 M (\()S FmE 55 0 :M f203 sf ( )S 57 0 :M FrMacBegin B 0 FmP F FmOP 168.963 522.666 M (a)S FmE 57 0 :M f148 sf ( )S 59 0 :M FrMacBegin B 0 FmP F FmOP 173.963 522.666 M (\) < )S FmE 60 0 :M f203 sf ( )S 62 0 :M FrMacBegin B 0 FmP F FmOP 187.931 522.666 M (C)S FmE 62 0 :M f148 sf ( )S 64 0 :M FrMacBegin B 0 FmP F FmOP 194.601 522.666 M (\()S FmE 65 0 :M f203 sf ( )S 67 0 :M FrMacBegin B 0 FmP F FmOP 197.928 522.666 M (b)S FmE 67 0 :M f148 sf ( )S 69 0 :M FrMacBegin B 0 FmP F FmOP 202.928 522.666 M (\) does )S FmE 70 0 :M f203 sf ( )S 72 0 :M FrMacBegin B 0 FmP F FmOP 229.583 522.666 M (not)S FmE 72 0 :M f148 sf ( )S 74 0 :M FrMacBegin B 0 FmP F FmOP 242.362 522.666 M ( mean )S FmE 75 0 :M f203 sf ( )S 77 0 :M FrMacBegin B 0 FmP F FmOP 269.017 522.666 M (a)S FmE 77 0 :M f148 sf ( )S 79 0 :M FrMacBegin B 0 FmP F FmOP 274.017 522.666 M ( )S FmE 80 0 :M f237 sf ( )S 82 0 :M FrMacBegin B 0 FmP F FmOP 276.517 522.666 M (\256)S FmE 82 0 :M f148 sf ( )S 84 0 :M FrMacBegin B 0 FmP F FmOP 286.385 522.666 M ( )S FmE 85 0 :M f203 sf ( )S 87 0 :M FrMacBegin B 0 FmP F FmOP 288.885 522.666 M (b)S FmE 87 0 :M f148 sf ( )S 89 0 :M FrMacBegin B 0 FmP F FmOP 76 534.666 M (d.)S 10.5 N (V)S -1.111 N (ector clocks and causal relation)S 76 546.666 M (e.)S 11.062 N (ordering of messages so you recei)S -0.251 N (v)S -0.151 N (e them in the order sent)S 94 558.666 M (i.)S 12.722 N (wh)S -0.051 N (y)S 94 570.666 M (ii.)S 9.943 N (for broadcast \(ISIS\): Birman-Schiper)S -0.2 N (-Stephenson)S 94 582.666 M (iii.)S 7.165 N (for point to point: Schiper)S -0.2 N (-Eggli-Sandoz)S 58 594.666 M (7.)S 10.5 N (Global state)S 76 606.666 M (a.)S 11.062 N (Sho)S -0.251 N (w problem of slicing state when something is in transit)S 76 618.666 M (b)S -0.4 N (.)S 10.9 N (De\336)S (ne local state; )S FmE 90 0 :M f203 sf ( )S 92 0 :M FrMacBegin B 0 FmP F FmOP 168.69 618.666 M (send)S FmE 92 0 :M f148 sf ( )S 94 0 :M FrMacBegin B 0 FmP F FmOP 187.018 618.666 M (\()S FmE 95 0 :M f203 sf ( )S 97 0 :M FrMacBegin B 0 FmP F FmOP 190.345 618.666 M (m)S FmE 97 0 :M f250 sf ( )S 99 0 :M FrMacBegin B 0 FmP F FmOP 197.564 621.166 M (ij)S FmE 99 0 :M f148 sf ( )S 101 0 :M FrMacBegin B 0 FmP F FmOP 202.01 618.666 M (\) )S FmE 102 0 :M f237 sf ( )S 104 0 :M FrMacBegin B 0 FmP F FmOP 207.837 618.666 M (\316)S FmE 104 0 :M f148 sf ( )S 106 0 :M FrMacBegin B 0 FmP F FmOP 214.966 618.666 M ( )S FmE 107 0 :M f203 sf ( )S 109 0 :M FrMacBegin B 0 FmP F FmOP 217.466 618.666 M (LS)S FmE 109 0 :M f250 sf ( )S 111 0 :M FrMacBegin B 0 FmP F FmOP 228.025 621.166 M (i)S FmE 111 0 :M f148 sf ( )S 113 0 :M FrMacBegin B 0 FmP F FmOP 230.248 618.666 M ( if)S -0.251 N (f time of )S FmE 114 0 :M f203 sf ( )S 116 0 :M FrMacBegin B 0 FmP F FmOP 275.531 618.666 M (send)S FmE 116 0 :M f148 sf ( )S 118 0 :M FrMacBegin B 0 FmP F FmOP 293.859 618.666 M (\()S FmE 119 0 :M f203 sf ( )S 121 0 :M FrMacBegin B 0 FmP F FmOP 297.187 618.666 M (m)S FmE 121 0 :M f250 sf ( )S 123 0 :M FrMacBegin B 0 FmP F FmOP 304.406 621.166 M (ij)S FmE 123 0 :M f148 sf ( )S 125 0 :M FrMacBegin B 0 FmP F FmOP 308.851 618.666 M (\) < current time of )S FmE 126 0 :M f203 sf ( )S 128 0 :M FrMacBegin B 0 FmP F FmOP 384.73 618.666 M (LS)S FmE 128 0 :M f250 sf ( )S 130 0 :M FrMacBegin B 0 FmP F FmOP 395.289 621.166 M (i)S FmE 130 0 :M f148 sf ( )S 132 0 :M FrMacBegin B 0 FmP F FmOP 397.512 618.666 M (; similar for recei)S -0.251 N (v)S -0.151 N (e)S 76 632.499 M (c.)S 11.062 N (transit\()S FmE 133 0 :M f203 sf ( )S 135 0 :M FrMacBegin B 0 FmP F FmOP 122.318 632.499 M (LS)S FmE 135 0 :M f250 sf ( )S 137 0 :M FrMacBegin B 0 FmP F FmOP 132.877 634.999 M (i)S FmE 137 0 :M f148 sf ( )S 139 0 :M FrMacBegin B 0 FmP F FmOP 135.1 632.499 M (, )S FmE 140 0 :M f203 sf ( )S 142 0 :M FrMacBegin B 0 FmP F FmOP 140.1 632.499 M (LS)S FmE 142 0 :M f250 sf ( )S 144 0 :M FrMacBegin B 0 FmP F FmOP 150.659 634.999 M (j)S FmE 144 0 :M f148 sf ( )S 146 0 :M FrMacBegin B 0 FmP F FmOP 152.881 632.499 M (\); inconsistent\()S FmE 147 0 :M f203 sf ( )S 149 0 :M FrMacBegin B 0 FmP F FmOP 212.583 632.499 M (LS)S FmE 149 0 :M f250 sf ( )S 151 0 :M FrMacBegin B 0 FmP F FmOP 223.143 634.999 M (i)S FmE 151 0 :M f148 sf ( )S 153 0 :M FrMacBegin B 0 FmP F FmOP 225.365 632.499 M (, )S FmE 154 0 :M f203 sf ( )S 156 0 :M FrMacBegin B 0 FmP F FmOP 230.365 632.499 M (LS)S FmE 156 0 :M f250 sf ( )S 158 0 :M FrMacBegin B 0 FmP F FmOP 240.924 634.999 M (j)S FmE 158 0 :M f148 sf ( )S 160 0 :M FrMacBegin B 0 FmP F FmOP 243.147 632.499 M (\); consistent state is one with inconsistent set empty for all pairs )S FmE 161 0 :M f203 sf ( )S 163 0 :M FrMacBegin B 0 FmP F FmOP 501.401 632.499 M (LS)S FmE 163 0 :M f250 sf ( )S 165 0 :M FrMacBegin B 0 FmP F FmOP 511.96 634.999 M (i)S FmE 165 0 :M f148 sf ( )S 167 0 :M FrMacBegin B 0 FmP F FmOP 514.183 632.499 M (, )S FmE 168 0 :M f203 sf ( )S 170 0 :M FrMacBegin B 0 FmP F FmOP 94 646.333 M (LS)S FmE 170 0 :M f250 sf ( )S 172 0 :M FrMacBegin B 0 FmP F FmOP 104.559 648.833 M (j)S FmE 172 0 :M f148 sf ( )S 174 0 :M FrMacBegin B 0 FmP F FmOP 76 660.166 M (d.)S 10.5 N (Consistent global state: Chandry-Lamport)S 58 672.166 M (8.)S 10.5 N (T)S -0.701 N (ermination detection)S 76 684.166 M (a.)S 11.062 N (Haung)S FmE endp showpage %%PageTrailer %%Page: 2 2 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 2 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 175 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 175 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 175 0 :M f148 sf ( )S 177 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Lamport\325s Clocks)S 114.027 N (ECS 251 \320 Winter 2001)S 159.015 N (Page )S (2)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 178 0 :M f175 sf ( )S 182 0 :M FrMacBegin B 0 FmP F FmOP 223.085 72 M (Lamport\325)S -0.668 N (s Clocks)S FmE 182 0 :M f263 sf ( )S 185 0 :M FrMacBegin B 0 FmP F FmOP 58 104 M (Intr)S -0.217 N (oduction)S FmE 185 0 :M f148 sf ( )S 187 0 :M FrMacBegin B 0 FmP F FmOP 58 121.667 M (Lamport\325)S -0.552 N (s clocks k)S -0.1 N (eep a virtual time among distrib)S -0.2 N (uted systems. )S -0.181 N (The goal is to pro)S -0.151 N (vide an ordering upon e)S -0.251 N (v)S -0.151 N (ents )S 58 133.667 M (within the system.)S FmE 188 0 :M f263 sf ( )S 191 0 :M FrMacBegin B 0 FmP F FmOP 58 159 M (Notation)S FmE 191 0 :M f148 sf ( )S 193 0 :M FrMacBegin B 0 FmP F FmOP 58 176.667 M (\245)S FmE 193 0 :M f203 sf ( )S 195 0 :M FrMacBegin B 0 FmP F FmOP 76 176.667 M (P)S FmE 196 0 :M f250 sf ( )S 198 0 :M FrMacBegin B 0 FmP F FmOP 82.108 179.167 M (i)S FmE 198 0 :M f148 sf ( )S 200 0 :M FrMacBegin B 0 FmP F FmOP 84.331 176.667 M ( process)S 58 190.5 M (\245)S FmE 200 0 :M f203 sf ( )S 202 0 :M FrMacBegin B 0 FmP F FmOP 76 190.5 M (C)S FmE 203 0 :M f250 sf ( )S 205 0 :M FrMacBegin B 0 FmP F FmOP 82.67 193 M (i)S FmE 205 0 :M f148 sf ( )S 207 0 :M FrMacBegin B 0 FmP F FmOP 84.893 190.5 M (. clock associated with process )S FmE 207 0 :M f203 sf ( )S 209 0 :M FrMacBegin B 0 FmP F FmOP 210.396 190.5 M (P)S FmE 210 0 :M f250 sf ( )S 212 0 :M FrMacBegin B 0 FmP F FmOP 216.504 193 M (i)S FmE 212 0 :M f263 sf ( )S 215 0 :M FrMacBegin B 0 FmP F FmOP 58 217.667 M (Pr)S -0.217 N (otocol)S FmE 215 0 :M f148 sf ( )S 217 0 :M FrMacBegin B 0 FmP F FmOP 58 233.333 M (1.)S 10.5 N (Increment clock )S FmE 217 0 :M f203 sf ( )S 219 0 :M FrMacBegin B 0 FmP F FmOP 143.183 233.333 M (C)S FmE 220 0 :M f250 sf ( )S 222 0 :M FrMacBegin B 0 FmP F FmOP 149.853 235.833 M (i)S FmE 222 0 :M f148 sf ( )S 224 0 :M FrMacBegin B 0 FmP F FmOP 152.075 233.333 M ( between an)S -0.151 N (y tw)S -0.1 N (o successi)S -0.251 N (v)S -0.151 N (e e)S -0.251 N (v)S -0.151 N (ents in process )S FmE 224 0 :M f203 sf ( )S 226 0 :M FrMacBegin B 0 FmP F FmOP 339.272 233.333 M (P)S FmE 227 0 :M f250 sf ( )S 229 0 :M FrMacBegin B 0 FmP F FmOP 345.381 235.833 M (i)S FmE 229 0 :M f148 sf ( )S 231 0 :M FrMacBegin B 0 FmP F FmOP 347.604 233.333 M (: )S FmE 231 0 :M f203 sf ( )S 233 0 :M FrMacBegin B 0 FmP F FmOP 352.882 233.333 M (C)S FmE 234 0 :M f250 sf ( )S 236 0 :M FrMacBegin B 0 FmP F FmOP 359.552 235.833 M (i)S FmE 236 0 :M f148 sf ( )S 238 0 :M FrMacBegin B 0 FmP F FmOP 361.774 233.333 M ( )S FmE 238 0 :M f237 sf ( )S 240 0 :M FrMacBegin B 0 FmP F FmOP 364.274 233.333 M (\254)S FmE 241 0 :M f148 sf ( )S 243 0 :M FrMacBegin B 0 FmP F FmOP 374.143 233.333 M ( )S FmE 243 0 :M f203 sf ( )S 245 0 :M FrMacBegin B 0 FmP F FmOP 376.643 233.333 M (C)S FmE 246 0 :M f250 sf ( )S 248 0 :M FrMacBegin B 0 FmP F FmOP 383.313 235.833 M (i)S FmE 248 0 :M f148 sf ( )S 250 0 :M FrMacBegin B 0 FmP F FmOP 385.535 233.333 M ( + )S FmE 250 0 :M f203 sf ( )S 252 0 :M FrMacBegin B 0 FmP F FmOP 396.175 233.333 M (d)S FmE 253 0 :M f148 sf ( )S 255 0 :M FrMacBegin B 0 FmP F FmOP 401.175 233.333 M ( \()S FmE 255 0 :M f203 sf ( )S 257 0 :M FrMacBegin B 0 FmP F FmOP 407.002 233.333 M (d)S FmE 258 0 :M f148 sf ( )S 260 0 :M FrMacBegin B 0 FmP F FmOP 412.002 233.333 M ( > 0\))S 58 250.133 M (2.)S 10.5 N -0.105(Let e)W -0.251 N (v)S -0.151 N -0.105(ent )W FmE 260 0 :M f203 sf ( )S 262 0 :M FrMacBegin B 0 FmP F FmOP 115.367 250.133 M (a)S FmE 263 0 :M f148 sf ( )S 265 0 :M FrMacBegin B 0 FmP F FmOP 120.367 250.133 M -0.105( be the sending of a message by process )W FmE 265 0 :M f203 sf ( )S 267 0 :M FrMacBegin B 0 FmP F FmOP 281.304 250.133 M (P)S FmE 268 0 :M f250 sf ( )S 270 0 :M FrMacBegin B 0 FmP F FmOP 287.412 252.633 M (i)S FmE 270 0 :M f148 sf ( )S 272 0 :M FrMacBegin B 0 FmP F FmOP 289.635 250.133 M -0.105(; the timestamp is )W FmE 272 0 :M f203 sf ( )S 274 0 :M FrMacBegin B 0 FmP F FmOP 362.534 250.133 M (t)S FmE 275 0 :M f250 sf ( )S 277 0 :M FrMacBegin B 0 FmP F FmOP 365.313 246.133 M (a)S FmE 277 0 :M f148 sf ( )S 279 0 :M FrMacBegin B 0 FmP F FmOP 369.313 250.133 M -0.105( = )W FmE 279 0 :M f203 sf ( )S 281 0 :M FrMacBegin B 0 FmP F FmOP 379.742 250.133 M (C)S FmE 282 0 :M f250 sf ( )S 284 0 :M FrMacBegin B 0 FmP F FmOP 386.412 252.633 M (i)S FmE 284 0 :M f148 sf ( )S 286 0 :M FrMacBegin B 0 FmP F FmOP 388.635 250.133 M (\()S FmE 286 0 :M f203 sf ( )S 288 0 :M FrMacBegin B 0 FmP F FmOP 391.962 250.133 M (a)S FmE 289 0 :M f148 sf ( )S 291 0 :M FrMacBegin B 0 FmP F FmOP 396.962 250.133 M -0.105(\) )W FmE 291 0 :M f203 sf ( )S 293 0 :M FrMacBegin B 0 FmP F FmOP 402.685 250.133 M (after)S FmE 294 0 :M f148 sf ( )S 296 0 :M FrMacBegin B 0 FmP F FmOP 421.569 250.133 M -0.105( the clock is incremented. )W 76 266.633 M (Let )S FmE 296 0 :M f203 sf ( )S 298 0 :M FrMacBegin B 0 FmP F FmOP 91.825 266.633 M (b)S FmE 299 0 :M f148 sf ( )S 301 0 :M FrMacBegin B 0 FmP F FmOP 96.825 266.633 M ( be the receipt of that message by )S FmE 301 0 :M f203 sf ( )S 303 0 :M FrMacBegin B 0 FmP F FmOP 232.875 266.633 M (P)S FmE 304 0 :M f250 sf ( )S 306 0 :M FrMacBegin B 0 FmP F FmOP 238.983 269.133 M (j)S FmE 306 0 :M f148 sf ( )S 308 0 :M FrMacBegin B 0 FmP F FmOP 241.206 266.633 M (. )S -0.181 N (Then when )S FmE 308 0 :M f203 sf ( )S 310 0 :M FrMacBegin B 0 FmP F FmOP 293.23 266.633 M (P)S FmE 311 0 :M f250 sf ( )S 313 0 :M FrMacBegin B 0 FmP F FmOP 299.338 269.133 M (j)S FmE 313 0 :M f148 sf ( )S 315 0 :M FrMacBegin B 0 FmP F FmOP 301.561 266.633 M ( recei)S -0.251 N (v)S -0.151 N (es the message, )S FmE 315 0 :M f203 sf ( )S 317 0 :M FrMacBegin B 0 FmP F FmOP 392.496 266.633 M (C)S FmE 318 0 :M f250 sf ( )S 320 0 :M FrMacBegin B 0 FmP F FmOP 399.166 269.133 M (j)S FmE 320 0 :M f148 sf ( )S 322 0 :M FrMacBegin B 0 FmP F FmOP 401.389 266.633 M ( )S FmE 322 0 :M f237 sf ( )S 324 0 :M FrMacBegin B 0 FmP F FmOP 403.889 266.633 M (\254)S FmE 325 0 :M f148 sf ( )S 327 0 :M FrMacBegin B 0 FmP F FmOP 413.757 266.633 M ( max\()S FmE 327 0 :M f203 sf ( )S 329 0 :M FrMacBegin B 0 FmP F FmOP 436.801 266.633 M (C)S FmE 330 0 :M f250 sf ( )S 332 0 :M FrMacBegin B 0 FmP F FmOP 443.471 269.133 M (j)S FmE 332 0 :M f148 sf ( )S 334 0 :M FrMacBegin B 0 FmP F FmOP 445.694 266.633 M (, )S FmE 334 0 :M f203 sf ( )S 336 0 :M FrMacBegin B 0 FmP F FmOP 450.694 266.633 M (t)S FmE 337 0 :M f250 sf ( )S 339 0 :M FrMacBegin B 0 FmP F FmOP 453.472 262.633 M (a)S FmE 339 0 :M f148 sf ( )S 341 0 :M FrMacBegin B 0 FmP F FmOP 457.472 266.633 M ( + )S FmE 341 0 :M f203 sf ( )S 343 0 :M FrMacBegin B 0 FmP F FmOP 468.112 266.633 M (d)S FmE 344 0 :M f148 sf ( )S 346 0 :M FrMacBegin B 0 FmP F FmOP 473.112 266.633 M (\) \()S FmE 346 0 :M f203 sf ( )S 348 0 :M FrMacBegin B 0 FmP F FmOP 482.267 266.633 M (d)S FmE 349 0 :M f148 sf ( )S 351 0 :M FrMacBegin B 0 FmP F FmOP 487.267 266.633 M ( > 0\))S FmE 351 0 :M f263 sf ( )S 354 0 :M FrMacBegin B 0 FmP F FmOP 58 293.799 M (Example)S FmE 354 0 :M f148 sf ( )S 356 0 :M FrMacBegin B 0 FmP F FmOP 58 455.466 M (Assume all clocks start at 0, and )S FmE 357 0 :M f203 sf ( )S 359 0 :M FrMacBegin B 0 FmP F FmOP 189.621 455.466 M (d)S FmE 359 0 :M f148 sf ( )S 361 0 :M FrMacBegin B 0 FmP F FmOP 194.621 455.466 M ( is 1 \(that is, each e)S -0.251 N (v)S -0.151 N (ent incrememts the clock by 1\). )S -0.181 N (The e)S -0.251 N (v)S -0.151 N (ents and clocks are:)S FmE 362 0 :M f203 sf ( )S 364 0 :M FrMacBegin B 0 FmP F FmOP 58 467.466 M (e)S FmE 364 0 :M f276 sf ( )S 366 0 :M FrMacBegin B 0 FmP F FmOP 62.438 469.966 M (11)S FmE 366 0 :M f148 sf ( )S 368 0 :M FrMacBegin B 0 FmP F FmOP 70.438 467.466 M (: )S FmE 369 0 :M f203 sf ( )S 371 0 :M FrMacBegin B 0 FmP F FmOP 75.717 467.466 M (C)S FmE 371 0 :M f276 sf ( )S 373 0 :M FrMacBegin B 0 FmP F FmOP 82.387 469.966 M (1)S FmE 373 0 :M f148 sf ( )S 375 0 :M FrMacBegin B 0 FmP F FmOP 86.387 467.466 M ( )S FmE 376 0 :M f237 sf ( )S 378 0 :M FrMacBegin B 0 FmP F FmOP 88.887 467.466 M (\254)S FmE 378 0 :M f148 sf ( )S 380 0 :M FrMacBegin B 0 FmP F FmOP 98.755 467.466 M ( 1)S FmE 381 0 :M f203 sf ( )S 383 0 :M FrMacBegin B 0 FmP F FmOP 58 483.966 M (e)S FmE 383 0 :M f276 sf ( )S 385 0 :M FrMacBegin B 0 FmP F FmOP 62.438 486.466 M (31)S FmE 385 0 :M f148 sf ( )S 387 0 :M FrMacBegin B 0 FmP F FmOP 70.438 483.966 M (: )S FmE 388 0 :M f203 sf ( )S 390 0 :M FrMacBegin B 0 FmP F FmOP 75.717 483.966 M (C)S FmE 390 0 :M f276 sf ( )S 392 0 :M FrMacBegin B 0 FmP F FmOP 82.387 486.466 M (3)S FmE 392 0 :M f148 sf ( )S 394 0 :M FrMacBegin B 0 FmP F FmOP 86.387 483.966 M ( )S FmE 395 0 :M f237 sf ( )S 397 0 :M FrMacBegin B 0 FmP F FmOP 88.887 483.966 M (\254)S FmE 397 0 :M f148 sf ( )S 399 0 :M FrMacBegin B 0 FmP F FmOP 98.755 483.966 M ( 1; timestamp )S FmE 400 0 :M f203 sf ( )S 402 0 :M FrMacBegin B 0 FmP F FmOP 155.691 483.966 M (t)S FmE 402 0 :M f276 sf ( )S 404 0 :M FrMacBegin B 0 FmP F FmOP 158.469 479.966 M (3,1)S FmE 404 0 :M f203 sf ( )S 406 0 :M FrMacBegin B 0 FmP F FmOP 168.469 483.966 M ( )S FmE 407 0 :M f148 sf ( )S 409 0 :M FrMacBegin B 0 FmP F FmOP 170.969 483.966 M (of message is 1)S FmE 409 0 :M f203 sf ( )S 411 0 :M FrMacBegin B 0 FmP F FmOP 58 500.466 M (e)S FmE 412 0 :M f276 sf ( )S 414 0 :M FrMacBegin B 0 FmP F FmOP 62.438 502.966 M (21)S FmE 414 0 :M f148 sf ( )S 416 0 :M FrMacBegin B 0 FmP F FmOP 70.438 500.466 M (: )S FmE 416 0 :M f203 sf ( )S 418 0 :M FrMacBegin B 0 FmP F FmOP 75.717 500.466 M (C)S FmE 419 0 :M f276 sf ( )S 421 0 :M FrMacBegin B 0 FmP F FmOP 82.387 502.966 M (2)S FmE 421 0 :M f148 sf ( )S 423 0 :M FrMacBegin B 0 FmP F FmOP 86.387 500.466 M ( )S FmE 423 0 :M f237 sf ( )S 425 0 :M FrMacBegin B 0 FmP F FmOP 88.887 500.466 M (\254)S FmE 426 0 :M f148 sf ( )S 428 0 :M FrMacBegin B 0 FmP F FmOP 98.755 500.466 M ( 2 as )S FmE 428 0 :M f203 sf ( )S 430 0 :M FrMacBegin B 0 FmP F FmOP 119.583 500.466 M (t)S FmE 431 0 :M f276 sf ( )S 433 0 :M FrMacBegin B 0 FmP F FmOP 122.361 496.466 M (3,1)S FmE 433 0 :M f148 sf ( )S 435 0 :M FrMacBegin B 0 FmP F FmOP 132.361 500.466 M ( = 1, after the increment )S FmE 435 0 :M f203 sf ( )S 437 0 :M FrMacBegin B 0 FmP F FmOP 233.506 500.466 M (C)S FmE 438 0 :M f276 sf ( )S 440 0 :M FrMacBegin B 0 FmP F FmOP 240.176 502.966 M (2)S FmE 440 0 :M f148 sf ( )S 442 0 :M FrMacBegin B 0 FmP F FmOP 244.176 500.466 M ( )S FmE 442 0 :M f237 sf ( )S 444 0 :M FrMacBegin B 0 FmP F FmOP 246.676 500.466 M (\254)S FmE 445 0 :M f148 sf ( )S 447 0 :M FrMacBegin B 0 FmP F FmOP 256.544 500.466 M ( 1, and )S FmE 447 0 :M f203 sf ( )S 449 0 :M FrMacBegin B 0 FmP F FmOP 285.982 500.466 M (C)S FmE 450 0 :M f276 sf ( )S 452 0 :M FrMacBegin B 0 FmP F FmOP 292.652 502.966 M (2)S FmE 452 0 :M f148 sf ( )S 454 0 :M FrMacBegin B 0 FmP F FmOP 296.652 500.466 M ( )S FmE 454 0 :M f237 sf ( )S 456 0 :M FrMacBegin B 0 FmP F FmOP 299.152 500.466 M (\254)S FmE 457 0 :M f148 sf ( )S 459 0 :M FrMacBegin B 0 FmP F FmOP 309.021 500.466 M ( max\()S FmE 459 0 :M f203 sf ( )S 461 0 :M FrMacBegin B 0 FmP F FmOP 332.065 500.466 M (C)S FmE 462 0 :M f276 sf ( )S 464 0 :M FrMacBegin B 0 FmP F FmOP 338.735 502.966 M (2)S FmE 464 0 :M f148 sf ( )S 466 0 :M FrMacBegin B 0 FmP F FmOP 342.735 500.466 M (, )S FmE 466 0 :M f203 sf ( )S 468 0 :M FrMacBegin B 0 FmP F FmOP 347.735 500.466 M (t)S FmE 469 0 :M f276 sf ( )S 471 0 :M FrMacBegin B 0 FmP F FmOP 350.513 496.466 M (3,1)S FmE 471 0 :M f148 sf ( )S 473 0 :M FrMacBegin B 0 FmP F FmOP 360.513 500.466 M ( + 1\) = max\(1, 1 + 1\) = max\(1, 2\) = 2)S FmE 473 0 :M f203 sf ( )S 475 0 :M FrMacBegin B 0 FmP F FmOP 58 516.966 M (e)S FmE 476 0 :M f276 sf ( )S 478 0 :M FrMacBegin B 0 FmP F FmOP 62.438 519.466 M (22)S FmE 478 0 :M f148 sf ( )S 480 0 :M FrMacBegin B 0 FmP F FmOP 70.438 516.966 M (: )S FmE 480 0 :M f203 sf ( )S 482 0 :M FrMacBegin B 0 FmP F FmOP 75.717 516.966 M (C)S FmE 483 0 :M f276 sf ( )S 485 0 :M FrMacBegin B 0 FmP F FmOP 82.387 519.466 M (2)S FmE 485 0 :M f148 sf ( )S 487 0 :M FrMacBegin B 0 FmP F FmOP 86.387 516.966 M ( )S FmE 487 0 :M f237 sf ( )S 489 0 :M FrMacBegin B 0 FmP F FmOP 88.887 516.966 M (\254)S FmE 490 0 :M f148 sf ( )S 492 0 :M FrMacBegin B 0 FmP F FmOP 98.755 516.966 M ( 3; timestamp )S FmE 492 0 :M f203 sf ( )S 494 0 :M FrMacBegin B 0 FmP F FmOP 155.691 516.966 M (t)S FmE 495 0 :M f276 sf ( )S 497 0 :M FrMacBegin B 0 FmP F FmOP 158.469 512.966 M (2,2)S FmE 497 0 :M f203 sf ( )S 499 0 :M FrMacBegin B 0 FmP F FmOP 168.469 516.966 M ( )S FmE 499 0 :M f148 sf ( )S 501 0 :M FrMacBegin B 0 FmP F FmOP 170.969 516.966 M (of message is 3)S FmE 502 0 :M f203 sf ( )S 504 0 :M FrMacBegin B 0 FmP F FmOP 58 533.465 M (e)S FmE 504 0 :M f276 sf ( )S 506 0 :M FrMacBegin B 0 FmP F FmOP 62.438 535.965 M (12)S FmE 506 0 :M f148 sf ( )S 508 0 :M FrMacBegin B 0 FmP F FmOP 70.438 533.465 M (: )S FmE 509 0 :M f203 sf ( )S 511 0 :M FrMacBegin B 0 FmP F FmOP 75.717 533.465 M (C)S FmE 511 0 :M f276 sf ( )S 513 0 :M FrMacBegin B 0 FmP F FmOP 82.387 535.965 M (1)S FmE 513 0 :M f148 sf ( )S 515 0 :M FrMacBegin B 0 FmP F FmOP 86.387 533.465 M ( )S FmE 516 0 :M f237 sf ( )S 518 0 :M FrMacBegin B 0 FmP F FmOP 88.887 533.465 M (\254)S FmE 518 0 :M f148 sf ( )S 520 0 :M FrMacBegin B 0 FmP F FmOP 98.755 533.465 M ( 2; timestamp )S FmE 521 0 :M f203 sf ( )S 523 0 :M FrMacBegin B 0 FmP F FmOP 155.691 533.465 M (t)S FmE 523 0 :M f276 sf ( )S 525 0 :M FrMacBegin B 0 FmP F FmOP 158.469 529.465 M (1,2)S FmE 525 0 :M f203 sf ( )S 527 0 :M FrMacBegin B 0 FmP F FmOP 168.469 533.465 M ( )S FmE 528 0 :M f148 sf ( )S 530 0 :M FrMacBegin B 0 FmP F FmOP 170.969 533.465 M (of message is 2)S FmE 530 0 :M f203 sf ( )S 532 0 :M FrMacBegin B 0 FmP F FmOP 58 549.965 M (e)S FmE 533 0 :M f276 sf ( )S 535 0 :M FrMacBegin B 0 FmP F FmOP 62.438 552.465 M (23)S FmE 535 0 :M f148 sf ( )S 537 0 :M FrMacBegin B 0 FmP F FmOP 70.438 549.965 M (: )S FmE 537 0 :M f203 sf ( )S 539 0 :M FrMacBegin B 0 FmP F FmOP 75.717 549.965 M (C)S FmE 540 0 :M f276 sf ( )S 542 0 :M FrMacBegin B 0 FmP F FmOP 82.387 552.465 M (2)S FmE 542 0 :M f148 sf ( )S 544 0 :M FrMacBegin B 0 FmP F FmOP 86.387 549.965 M ( )S FmE 544 0 :M f237 sf ( )S 546 0 :M FrMacBegin B 0 FmP F FmOP 88.887 549.965 M (\254)S FmE 547 0 :M f148 sf ( )S 549 0 :M FrMacBegin B 0 FmP F FmOP 98.755 549.965 M ( 4 as )S FmE 549 0 :M f203 sf ( )S 551 0 :M FrMacBegin B 0 FmP F FmOP 119.583 549.965 M (t)S FmE 552 0 :M f276 sf ( )S 554 0 :M FrMacBegin B 0 FmP F FmOP 122.361 545.965 M (1,2)S FmE 554 0 :M f148 sf ( )S 556 0 :M FrMacBegin B 0 FmP F FmOP 132.361 549.965 M ( = 2, after the increment )S FmE 556 0 :M f203 sf ( )S 558 0 :M FrMacBegin B 0 FmP F FmOP 233.506 549.965 M (C)S FmE 559 0 :M f276 sf ( )S 561 0 :M FrMacBegin B 0 FmP F FmOP 240.176 552.465 M (2)S FmE 561 0 :M f148 sf ( )S 563 0 :M FrMacBegin B 0 FmP F FmOP 244.176 549.965 M ( )S FmE 563 0 :M f237 sf ( )S 565 0 :M FrMacBegin B 0 FmP F FmOP 246.676 549.965 M (\254)S FmE 566 0 :M f148 sf ( )S 568 0 :M FrMacBegin B 0 FmP F FmOP 256.544 549.965 M ( 4, and )S FmE 568 0 :M f203 sf ( )S 570 0 :M FrMacBegin B 0 FmP F FmOP 285.982 549.965 M (C)S FmE 571 0 :M f276 sf ( )S 573 0 :M FrMacBegin B 0 FmP F FmOP 292.652 552.465 M (2)S FmE 573 0 :M f148 sf ( )S 575 0 :M FrMacBegin B 0 FmP F FmOP 296.652 549.965 M ( )S FmE 575 0 :M f237 sf ( )S 577 0 :M FrMacBegin B 0 FmP F FmOP 299.152 549.965 M (\254)S FmE 578 0 :M f148 sf ( )S 580 0 :M FrMacBegin B 0 FmP F FmOP 309.021 549.965 M ( max\()S FmE 580 0 :M f203 sf ( )S 582 0 :M FrMacBegin B 0 FmP F FmOP 332.065 549.965 M (C)S FmE 583 0 :M f276 sf ( )S 585 0 :M FrMacBegin B 0 FmP F FmOP 338.735 552.465 M (2)S FmE 585 0 :M f148 sf ( )S 587 0 :M FrMacBegin B 0 FmP F FmOP 342.735 549.965 M (, )S FmE 587 0 :M f203 sf ( )S 589 0 :M FrMacBegin B 0 FmP F FmOP 347.735 549.965 M (t)S FmE 590 0 :M f276 sf ( )S 592 0 :M FrMacBegin B 0 FmP F FmOP 350.513 545.965 M (1,2)S FmE 592 0 :M f148 sf ( )S 594 0 :M FrMacBegin B 0 FmP F FmOP 360.513 549.965 M ( + 1\) = max\(4, 2 + 1\) = max\(4, 2\) = 4)S FmE 594 0 :M f203 sf ( )S 596 0 :M FrMacBegin B 0 FmP F FmOP 58 566.465 M (e)S FmE 597 0 :M f276 sf ( )S 599 0 :M FrMacBegin B 0 FmP F FmOP 62.438 568.965 M (24)S FmE 599 0 :M f148 sf ( )S 601 0 :M FrMacBegin B 0 FmP F FmOP 70.438 566.465 M (: )S FmE 601 0 :M f203 sf ( )S 603 0 :M FrMacBegin B 0 FmP F FmOP 75.717 566.465 M (C)S FmE 604 0 :M f276 sf ( )S 606 0 :M FrMacBegin B 0 FmP F FmOP 82.387 568.965 M (2)S FmE 606 0 :M f148 sf ( )S 608 0 :M FrMacBegin B 0 FmP F FmOP 86.387 566.465 M ( )S FmE 608 0 :M f237 sf ( )S 610 0 :M FrMacBegin B 0 FmP F FmOP 88.887 566.465 M (\254)S FmE 611 0 :M f148 sf ( )S 613 0 :M FrMacBegin B 0 FmP F FmOP 98.755 566.465 M ( 5; timestamp )S FmE 613 0 :M f203 sf ( )S 615 0 :M FrMacBegin B 0 FmP F FmOP 155.691 566.465 M (t)S FmE 616 0 :M f276 sf ( )S 618 0 :M FrMacBegin B 0 FmP F FmOP 158.469 562.465 M (2,4)S FmE 618 0 :M f203 sf ( )S 620 0 :M FrMacBegin B 0 FmP F FmOP 168.469 566.465 M ( )S FmE 620 0 :M f148 sf ( )S 622 0 :M FrMacBegin B 0 FmP F FmOP 170.969 566.465 M (of message is 5)S FmE 623 0 :M f203 sf ( )S 625 0 :M FrMacBegin B 0 FmP F FmOP 58 582.965 M (e)S FmE 625 0 :M f276 sf ( )S 627 0 :M FrMacBegin B 0 FmP F FmOP 62.438 585.465 M (13)S FmE 627 0 :M f148 sf ( )S 629 0 :M FrMacBegin B 0 FmP F FmOP 70.438 582.965 M (: )S FmE 630 0 :M f203 sf ( )S 632 0 :M FrMacBegin B 0 FmP F FmOP 75.717 582.965 M (C)S FmE 632 0 :M f276 sf ( )S 634 0 :M FrMacBegin B 0 FmP F FmOP 82.387 585.465 M (1)S FmE 634 0 :M f148 sf ( )S 636 0 :M FrMacBegin B 0 FmP F FmOP 86.387 582.965 M ( )S FmE 637 0 :M f237 sf ( )S 639 0 :M FrMacBegin B 0 FmP F FmOP 88.887 582.965 M (\254)S FmE 639 0 :M f148 sf ( )S 641 0 :M FrMacBegin B 0 FmP F FmOP 98.755 582.965 M ( 4 as )S FmE 642 0 :M f203 sf ( )S 644 0 :M FrMacBegin B 0 FmP F FmOP 119.583 582.965 M (t)S FmE 644 0 :M f276 sf ( )S 646 0 :M FrMacBegin B 0 FmP F FmOP 122.361 578.965 M (2,2)S FmE 646 0 :M f148 sf ( )S 648 0 :M FrMacBegin B 0 FmP F FmOP 132.361 582.965 M ( = 3, after the increment )S FmE 649 0 :M f203 sf ( )S 651 0 :M FrMacBegin B 0 FmP F FmOP 233.506 582.965 M (C)S FmE 651 0 :M f276 sf ( )S 653 0 :M FrMacBegin B 0 FmP F FmOP 240.176 585.465 M (1)S FmE 653 0 :M f148 sf ( )S 655 0 :M FrMacBegin B 0 FmP F FmOP 244.176 582.965 M ( )S FmE 656 0 :M f237 sf ( )S 658 0 :M FrMacBegin B 0 FmP F FmOP 246.676 582.965 M (\254)S FmE 658 0 :M f148 sf ( )S 660 0 :M FrMacBegin B 0 FmP F FmOP 256.544 582.965 M ( 3, and )S FmE 661 0 :M f203 sf ( )S 663 0 :M FrMacBegin B 0 FmP F FmOP 285.982 582.965 M (C)S FmE 663 0 :M f276 sf ( )S 665 0 :M FrMacBegin B 0 FmP F FmOP 292.652 585.465 M (1)S FmE 665 0 :M f148 sf ( )S 667 0 :M FrMacBegin B 0 FmP F FmOP 296.652 582.965 M ( )S FmE 668 0 :M f237 sf ( )S 670 0 :M FrMacBegin B 0 FmP F FmOP 299.152 582.965 M (\254)S FmE 670 0 :M f148 sf ( )S 672 0 :M FrMacBegin B 0 FmP F FmOP 309.021 582.965 M ( max\()S FmE 673 0 :M f203 sf ( )S 675 0 :M FrMacBegin B 0 FmP F FmOP 332.065 582.965 M (C)S FmE 675 0 :M f276 sf ( )S 677 0 :M FrMacBegin B 0 FmP F FmOP 338.735 585.465 M (1)S FmE 677 0 :M f148 sf ( )S 679 0 :M FrMacBegin B 0 FmP F FmOP 342.735 582.965 M (, )S FmE 680 0 :M f203 sf ( )S 682 0 :M FrMacBegin B 0 FmP F FmOP 347.735 582.965 M (t)S FmE 682 0 :M f276 sf ( )S 684 0 :M FrMacBegin B 0 FmP F FmOP 350.513 578.965 M (2,2)S FmE 684 0 :M f148 sf ( )S 686 0 :M FrMacBegin B 0 FmP F FmOP 360.513 582.965 M ( + 1\) = max\(3, 3 + 1\) = max\(3, 4\) = 4)S FmE 687 0 :M f203 sf ( )S 689 0 :M FrMacBegin B 0 FmP F FmOP 58 599.465 M (e)S FmE 689 0 :M f276 sf ( )S 691 0 :M FrMacBegin B 0 FmP F FmOP 62.438 601.965 M (32)S FmE 691 0 :M f148 sf ( )S 693 0 :M FrMacBegin B 0 FmP F FmOP 70.438 599.465 M (: )S FmE 694 0 :M f203 sf ( )S 696 0 :M FrMacBegin B 0 FmP F FmOP 75.717 599.465 M (C)S FmE 696 0 :M f276 sf ( )S 698 0 :M FrMacBegin B 0 FmP F FmOP 82.387 601.965 M (3)S FmE 698 0 :M f148 sf ( )S 700 0 :M FrMacBegin B 0 FmP F FmOP 86.387 599.465 M ( )S FmE 701 0 :M f237 sf ( )S 703 0 :M FrMacBegin B 0 FmP F FmOP 88.887 599.465 M (\254)S FmE 703 0 :M f148 sf ( )S 705 0 :M FrMacBegin B 0 FmP F FmOP 98.755 599.465 M ( 6 as )S FmE 706 0 :M f203 sf ( )S 708 0 :M FrMacBegin B 0 FmP F FmOP 119.583 599.465 M (t)S FmE 708 0 :M f276 sf ( )S 710 0 :M FrMacBegin B 0 FmP F FmOP 122.361 595.465 M (2,4)S FmE 710 0 :M f148 sf ( )S 712 0 :M FrMacBegin B 0 FmP F FmOP 132.361 599.465 M ( = 5, after the increment )S FmE 713 0 :M f203 sf ( )S 715 0 :M FrMacBegin B 0 FmP F FmOP 233.506 599.465 M (C)S FmE 715 0 :M f276 sf ( )S 717 0 :M FrMacBegin B 0 FmP F FmOP 240.176 601.965 M (3)S FmE 717 0 :M f148 sf ( )S 719 0 :M FrMacBegin B 0 FmP F FmOP 244.176 599.465 M ( )S FmE 720 0 :M f237 sf ( )S 722 0 :M FrMacBegin B 0 FmP F FmOP 246.676 599.465 M (\254)S FmE 722 0 :M f148 sf ( )S 724 0 :M FrMacBegin B 0 FmP F FmOP 256.544 599.465 M ( 2, and )S FmE 725 0 :M f203 sf ( )S 727 0 :M FrMacBegin B 0 FmP F FmOP 285.982 599.465 M (C)S FmE 727 0 :M f276 sf ( )S 729 0 :M FrMacBegin B 0 FmP F FmOP 292.652 601.965 M (3)S FmE 729 0 :M f148 sf ( )S 731 0 :M FrMacBegin B 0 FmP F FmOP 296.652 599.465 M ( )S FmE 732 0 :M f237 sf ( )S 734 0 :M FrMacBegin B 0 FmP F FmOP 299.152 599.465 M (\254)S FmE 734 0 :M f148 sf ( )S 736 0 :M FrMacBegin B 0 FmP F FmOP 309.021 599.465 M ( max\()S FmE 737 0 :M f203 sf ( )S 739 0 :M FrMacBegin B 0 FmP F FmOP 332.065 599.465 M (C)S FmE 739 0 :M f276 sf ( )S 741 0 :M FrMacBegin B 0 FmP F FmOP 338.735 601.965 M (3)S FmE 741 0 :M f148 sf ( )S 743 0 :M FrMacBegin B 0 FmP F FmOP 342.735 599.465 M (, )S FmE 744 0 :M f203 sf ( )S 746 0 :M FrMacBegin B 0 FmP F FmOP 347.735 599.465 M (t)S FmE 746 0 :M f276 sf ( )S 748 0 :M FrMacBegin B 0 FmP F FmOP 350.513 595.465 M (2,4)S FmE 748 0 :M f148 sf ( )S 750 0 :M FrMacBegin B 0 FmP F FmOP 360.513 599.465 M ( + 1\) = max\(2, 5 + 1\) = max\(2, 6\) = 6)S FmE 751 0 :M f263 sf ( )S 754 0 :M FrMacBegin B 0 FmP F FmOP 58 626.631 M (Pr)S -0.217 N (oblem)S FmE 754 0 :M f148 sf ( )S 756 0 :M FrMacBegin B 0 FmP F FmOP 58 644.298 M (Clearly)S -0.652 N (, if a )S FmE 756 0 :M f237 sf ( )S 758 0 :M FrMacBegin B 0 FmP F FmOP 107.324 644.298 M (\256)S FmE 759 0 :M f148 sf ( )S 761 0 :M FrMacBegin B 0 FmP F FmOP 117.192 644.298 M ( b, then )S FmE 761 0 :M f203 sf ( )S 763 0 :M FrMacBegin B 0 FmP F FmOP 149.409 644.298 M (C)S FmE 764 0 :M f148 sf ( )S 766 0 :M FrMacBegin B 0 FmP F FmOP 156.079 644.298 M (\()S FmE 766 0 :M f203 sf ( )S 768 0 :M FrMacBegin B 0 FmP F FmOP 159.406 644.298 M (a)S FmE 769 0 :M f148 sf ( )S 771 0 :M FrMacBegin B 0 FmP F FmOP 164.406 644.298 M (\) < )S FmE 771 0 :M f203 sf ( )S 773 0 :M FrMacBegin B 0 FmP F FmOP 178.374 644.298 M (C)S FmE 774 0 :M f148 sf ( )S 776 0 :M FrMacBegin B 0 FmP F FmOP 185.043 644.298 M (\()S FmE 776 0 :M f203 sf ( )S 778 0 :M FrMacBegin B 0 FmP F FmOP 188.371 644.298 M (b)S FmE 779 0 :M f148 sf ( )S 781 0 :M FrMacBegin B 0 FmP F FmOP 193.371 644.298 M (\). But if )S FmE 781 0 :M f203 sf ( )S 783 0 :M FrMacBegin B 0 FmP F FmOP 227.253 644.298 M (C)S FmE 784 0 :M f148 sf ( )S 786 0 :M FrMacBegin B 0 FmP F FmOP 233.923 644.298 M (\()S FmE 786 0 :M f203 sf ( )S 788 0 :M FrMacBegin B 0 FmP F FmOP 237.25 644.298 M (a)S FmE 789 0 :M f148 sf ( )S 791 0 :M FrMacBegin B 0 FmP F FmOP 242.25 644.298 M (\) < )S FmE 791 0 :M f203 sf ( )S 793 0 :M FrMacBegin B 0 FmP F FmOP 256.218 644.298 M (C)S FmE 794 0 :M f148 sf ( )S 796 0 :M FrMacBegin B 0 FmP F FmOP 262.888 644.298 M (\()S FmE 796 0 :M f203 sf ( )S 798 0 :M FrMacBegin B 0 FmP F FmOP 266.215 644.298 M (b)S FmE 799 0 :M f148 sf ( )S 801 0 :M FrMacBegin B 0 FmP F FmOP 271.215 644.298 M (\), does )S FmE 801 0 :M f203 sf ( )S 803 0 :M FrMacBegin B 0 FmP F FmOP 300.371 644.298 M (a)S FmE 804 0 :M f148 sf ( )S 806 0 :M FrMacBegin B 0 FmP F FmOP 305.371 644.298 M ( )S FmE 806 0 :M f237 sf ( )S 808 0 :M FrMacBegin B 0 FmP F FmOP 307.871 644.298 M (\256)S FmE 809 0 :M f148 sf ( )S 811 0 :M FrMacBegin B 0 FmP F FmOP 317.739 644.298 M ( )S FmE 811 0 :M f203 sf ( )S 813 0 :M FrMacBegin B 0 FmP F FmOP 320.239 644.298 M (b)S FmE 814 0 :M f148 sf ( )S 816 0 :M FrMacBegin B 0 FmP F FmOP 325.239 644.298 M (?)S 58 656.298 M -0.211(The answer)W -0.4 N -0.211(, surprisingly)W -0.652 N -0.211(, is not necessarily)W -0.652 N -0.211(. In the abo)W -0.151 N (v)S -0.151 N -0.211(e e)W -0.151 N -0.211(xample, )W FmE 816 0 :M f203 sf ( )S 818 0 :M FrMacBegin B 0 FmP F FmOP 322.519 656.298 M (C)S FmE 819 0 :M f276 sf ( )S 821 0 :M FrMacBegin B 0 FmP F FmOP 329.189 658.798 M (3)S FmE 821 0 :M f148 sf ( )S 823 0 :M FrMacBegin B 0 FmP F FmOP 333.189 656.298 M (\()S FmE 823 0 :M f203 sf ( )S 825 0 :M FrMacBegin B 0 FmP F FmOP 336.517 656.298 M (e)S FmE 826 0 :M f276 sf ( )S 828 0 :M FrMacBegin B 0 FmP F FmOP 340.955 658.798 M (31)S FmE 828 0 :M f148 sf ( )S 830 0 :M FrMacBegin B 0 FmP F FmOP 348.955 656.298 M -0.211(\) = 1 < 2 = )W FmE 830 0 :M f203 sf ( )S 832 0 :M FrMacBegin B 0 FmP F FmOP 392.938 656.298 M (C)S FmE 833 0 :M f276 sf ( )S 835 0 :M FrMacBegin B 0 FmP F FmOP 399.607 658.798 M (1)S FmE 835 0 :M f148 sf ( )S 837 0 :M FrMacBegin B 0 FmP F FmOP 403.607 656.298 M (\()S FmE 837 0 :M f203 sf ( )S 839 0 :M FrMacBegin B 0 FmP F FmOP 406.935 656.298 M (e)S FmE 840 0 :M f276 sf ( )S 842 0 :M FrMacBegin B 0 FmP F FmOP 411.374 658.798 M (12)S FmE 842 0 :M f148 sf ( )S 844 0 :M FrMacBegin B 0 FmP F FmOP 419.374 656.298 M -0.211(\). But )W FmE 844 0 :M f203 sf ( )S 846 0 :M FrMacBegin B 0 FmP F FmOP 444.228 656.298 M (e)S FmE 847 0 :M f276 sf ( )S 849 0 :M FrMacBegin B 0 FmP F FmOP 448.667 658.798 M (31)S FmE 849 0 :M f148 sf ( )S 851 0 :M FrMacBegin B 0 FmP F FmOP 456.667 656.298 M -0.211( and )W FmE 851 0 :M f203 sf ( )S 853 0 :M FrMacBegin B 0 FmP F FmOP 475.684 656.298 M (e)S FmE 854 0 :M f276 sf ( )S 856 0 :M FrMacBegin B 0 FmP F FmOP 480.122 658.798 M (12)S FmE 856 0 :M f148 sf ( )S 858 0 :M FrMacBegin B 0 FmP F FmOP 488.122 656.298 M -0.211( are caus-)W 58 670.131 M (ally unrelated; that is, )S FmE 858 0 :M f203 sf ( )S 860 0 :M FrMacBegin B 0 FmP F FmOP 147.136 670.131 M (e)S FmE 861 0 :M f276 sf ( )S 863 0 :M FrMacBegin B 0 FmP F FmOP 151.574 672.631 M (31)S FmE 863 0 :M f148 sf ( )S 865 0 :M FrMacBegin B 0 FmP F FmOP 159.574 670.131 M ( )S FmE 865 0 :M f237 sf ( )S 867 0 :M FrMacBegin B 0 FmP F FmOP 162.074 670.131 M (\256)S -8 N (/)S FmE 868 0 :M f203 sf ( )S 870 0 :M FrMacBegin B 0 FmP F FmOP 174.721 670.131 M (e)S FmE 870 0 :M f276 sf ( )S 872 0 :M FrMacBegin B 0 FmP F FmOP 179.159 672.631 M (12)S FmE 872 0 :M f148 sf ( )S 874 0 :M FrMacBegin B 0 FmP F FmOP 187.159 670.131 M (. Ho)S -0.251 N (we)S -0.251 N (v)S -0.151 N (er)S -0.4 N (, )S FmE 875 0 :M f203 sf ( )S 877 0 :M FrMacBegin B 0 FmP F FmOP 232.748 670.131 M (C)S FmE 877 0 :M f276 sf ( )S 879 0 :M FrMacBegin B 0 FmP F FmOP 239.417 672.631 M (1)S FmE 879 0 :M f148 sf ( )S 881 0 :M FrMacBegin B 0 FmP F FmOP 243.417 670.131 M (\()S FmE 882 0 :M f203 sf ( )S 884 0 :M FrMacBegin B 0 FmP F FmOP 246.745 670.131 M (e)S FmE 884 0 :M f276 sf ( )S 886 0 :M FrMacBegin B 0 FmP F FmOP 251.184 672.631 M (11)S FmE 886 0 :M f148 sf ( )S 888 0 :M FrMacBegin B 0 FmP F FmOP 259.184 670.131 M (\) = 1 < 6 = )S FmE 889 0 :M f203 sf ( )S 891 0 :M FrMacBegin B 0 FmP F FmOP 304.43 670.131 M (C)S FmE 891 0 :M f276 sf ( )S 893 0 :M FrMacBegin B 0 FmP F FmOP 311.1 672.631 M (3)S FmE 893 0 :M f148 sf ( )S 895 0 :M FrMacBegin B 0 FmP F FmOP 315.1 670.131 M (\()S FmE 896 0 :M f203 sf ( )S 898 0 :M FrMacBegin B 0 FmP F FmOP 318.428 670.131 M (e)S FmE 898 0 :M f276 sf ( )S 900 0 :M FrMacBegin B 0 FmP F FmOP 322.866 672.631 M (32)S FmE 900 0 :M f148 sf ( )S 902 0 :M FrMacBegin B 0 FmP F FmOP 330.866 670.131 M (\), and clearly )S FmE 903 0 :M f203 sf ( )S 905 0 :M FrMacBegin B 0 FmP F FmOP 385.832 670.131 M (e)S FmE 905 0 :M f276 sf ( )S 907 0 :M FrMacBegin B 0 FmP F FmOP 390.271 672.631 M (11)S FmE 907 0 :M f148 sf ( )S 909 0 :M FrMacBegin B 0 FmP F FmOP 398.271 670.131 M ( )S FmE 910 0 :M f237 sf ( )S 912 0 :M FrMacBegin B 0 FmP F FmOP 400.771 670.131 M (\256)S FmE 912 0 :M f148 sf ( )S 914 0 :M FrMacBegin B 0 FmP F FmOP 410.639 670.131 M ( )S FmE 915 0 :M f203 sf ( )S 917 0 :M FrMacBegin B 0 FmP F FmOP 413.139 670.131 M (e)S FmE 917 0 :M f276 sf ( )S 919 0 :M FrMacBegin B 0 FmP F FmOP 417.577 672.631 M (32)S FmE 919 0 :M f148 sf ( )S 921 0 :M FrMacBegin B 0 FmP F FmOP 425.577 670.131 M (. Hence one cannot say )S 58 683.964 M (one w)S -0.1 N (ay or the other)S -0.552 N (.)S FmE 58 297 468 145 rC 922 0 :M FrMacBegin 58 297.799 468 144 FmKp B 0 FmP F FmOP 94 324.799 FmB 378 0 FmL 2 1 FmSo 94 360.799 FmB 378 0 FmL 2 1 FmSo 94 405.799 FmB 378 0 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 125.5 324.299 FmAF T 0 360 4.5 4.5 0 125.5 324.299 2 1 F FmAP 0 360 4.5 4.5 0 T 241.5 324.966 FmAF T 0 360 4.5 4.5 0 241.5 324.966 2 1 F FmAP 0 360 4.5 4.5 0 T 182.833 360.966 FmAF T 0 360 4.5 4.5 0 182.833 360.966 2 1 F FmAP 0 360 4.5 4.5 0 T 233.5 360.966 FmAF T 0 360 4.5 4.5 0 233.5 360.966 2 1 F FmAP 0 360 4.5 4.5 0 T 145.5 406.966 FmAF T 0 360 4.5 4.5 0 145.5 406.966 2 1 F FmAP 0 360 4.5 4.5 0 T 347.5 360.966 FmAF T 0 360 4.5 4.5 0 347.5 360.966 2 1 F FmAP 0 360 4.5 4.5 0 T 421.5 406.299 FmAF T 0 360 4.5 4.5 0 421.5 406.299 2 1 F FmAP 0 360 4.5 4.5 0 T 418.833 325.633 FmAF T 0 360 4.5 4.5 0 418.833 325.633 2 1 F FmAP FmE 922 0 :M f289 sf ( )S 925 0 :M FrMacBegin 58 297.799 468 144 FmKp B 0 FmP F FmOP 73.333 325.167 M (P)S FmE 925 0 :M f148 sf ( )S 927 0 :M FrMacBegin 58 297.799 468 144 FmKp B 0 FmP F FmOP FmG 80.663 328.167 M 0.96 0.96 scale (1)S FmR FmE 928 0 :M f289 sf ( )S 931 0 :M FrMacBegin 58 297.799 468 144 FmKp B 0 FmP F FmOP 73.333 362.5 M (P)S FmE 931 0 :M f148 sf ( )S 933 0 :M FrMacBegin 58 297.799 468 144 FmKp B 0 FmP F FmOP FmG 80.663 365.5 M 0.96 0.96 scale (2)S FmR FmE 933 0 :M f289 sf ( )S 936 0 :M FrMacBegin 58 297.799 468 144 FmKp B 0 FmP F FmOP 73.333 409.167 M (P)S FmE 936 0 :M f148 sf ( )S 938 0 :M FrMacBegin 58 297.799 468 144 FmKp B 0 FmP F FmOP FmG 80.663 412.167 M 0.96 0.96 scale (3)S FmR FmG 122 316.833 M 0.96 0.96 scale (e11)S FmR FmG 241.333 318.833 M 0.96 0.96 scale (e12)S FmR FmG 180.667 353.5 M 0.96 0.96 scale (e21)S FmR FmG 234 353.5 M 0.96 0.96 scale (e22)S FmR FmG 324 353.5 M 0.96 0.96 scale (e23)S FmR FmG 129.333 398.167 M 0.96 0.96 scale (e31)S FmR FmG 420 398.833 M 0.96 0.96 scale (e32)S FmR FmG 412.667 318.167 M 0.96 0.96 scale (e13)S FmR 309.693 352.127 FmB 1.257 -3.235 FmL 10.027 7.618 FmL -12.54 -1.147 FmL 1 FmS 309.693 352.127 FmB 1.257 -3.235 FmL 10.027 7.618 FmL -12.54 -1.147 FmL FmFl 242 325.833 FmB 67.227 26.113 FmL 2 1 FmSo 400.972 328.971 FmB -0.616 -3.416 FmL 12.529 1.266 FmL -11.296 5.565 FmL 1 FmS 400.972 328.971 FmB -0.616 -3.416 FmL 12.529 1.266 FmL -11.296 5.565 FmL FmFl 237.333 358.5 FmB 163.146 -29.44 FmL 2 1 FmSo 405.241 395.607 FmB 1.719 -3.015 FmL 8.798 9.01 FmL -12.235 -2.979 FmL 1 FmS 405.241 395.607 FmB 1.719 -3.015 FmL 8.798 9.01 FmL -12.235 -2.979 FmL FmFl 350.667 364.5 FmB 54.14 30.86 FmL 2 1 FmSo 172.319 374.438 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL 1 FmS 172.319 374.438 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL FmFl 147.333 403.833 FmB 24.662 -29.014 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 324.167 360.966 FmAF T 0 360 4.5 4.5 0 324.167 360.966 2 1 F FmAP 355.333 351.167 M (e24)S FmE endp showpage %%PageTrailer %%Page: 3 3 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 3 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 939 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 939 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 939 0 :M f148 sf ( )S 941 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Vector Clocks)S 128.473 N (ECS 251 \320 Winter 2001)S 159.015 N (Page )S (3)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 942 0 :M f175 sf ( )S 946 0 :M FrMacBegin B 0 FmP F FmOP 238.668 72 M (V)S -1.802 N (ector Clocks)S FmE 946 0 :M f263 sf ( )S 949 0 :M FrMacBegin B 0 FmP F FmOP 58 104 M (Intr)S -0.217 N (oduction)S FmE 949 0 :M f148 sf ( )S 951 0 :M FrMacBegin B 0 FmP F FmOP 58 121.667 M (This is based upon Lamport\325)S -0.552 N (s clocks, b)S -0.2 N (ut each process k)S -0.1 N (eeps track of what is belie)S -0.251 N (v)S -0.151 N (es the other processes\325)S -0.742 N ( interrnal )S 58 133.667 M (clocks are \(hence the name, v)S -0.151 N (ector clocks\). )S -0.181 N (The goal is to pro)S -0.151 N (vide an ordering upon e)S -0.251 N (v)S -0.151 N (ents within the system.)S FmE 952 0 :M f263 sf ( )S 955 0 :M FrMacBegin B 0 FmP F FmOP 58 159 M (Notation)S FmE 955 0 :M f148 sf ( )S 957 0 :M FrMacBegin B 0 FmP F FmOP 58 176.667 M (\245)S FmE 957 0 :M f203 sf ( )S 959 0 :M FrMacBegin B 0 FmP F FmOP 76 176.667 M (n)S FmE 960 0 :M f148 sf ( )S 962 0 :M FrMacBegin B 0 FmP F FmOP 81 176.667 M ( processes)S 58 188.667 M (\245)S FmE 962 0 :M f203 sf ( )S 964 0 :M FrMacBegin B 0 FmP F FmOP 76 188.667 M (P)S FmE 965 0 :M f250 sf ( )S 967 0 :M FrMacBegin B 0 FmP F FmOP 82.108 191.167 M (i)S FmE 967 0 :M f148 sf ( )S 969 0 :M FrMacBegin B 0 FmP F FmOP 84.331 188.667 M ( process)S 58 202.5 M (\245)S FmE 969 0 :M f203 sf ( )S 971 0 :M FrMacBegin B 0 FmP F FmOP 76 202.5 M (C)S FmE 972 0 :M f250 sf ( )S 974 0 :M FrMacBegin B 0 FmP F FmOP 82.67 205 M (i)S FmE 974 0 :M f148 sf ( )S 976 0 :M FrMacBegin B 0 FmP F FmOP 84.893 202.5 M -0.013(. v)W -0.151 N -0.013(ector clock associated with process )W FmE 976 0 :M f203 sf ( )S 978 0 :M FrMacBegin B 0 FmP F FmOP 237.65 202.5 M (P)S FmE 979 0 :M f250 sf ( )S 981 0 :M FrMacBegin B 0 FmP F FmOP 243.759 205 M (i)S FmE 981 0 :M f148 sf ( )S 983 0 :M FrMacBegin B 0 FmP F FmOP 245.981 202.5 M -0.013(; )W FmE 983 0 :M f203 sf ( )S 985 0 :M FrMacBegin B 0 FmP F FmOP 251.247 202.5 M (j)S FmE 986 0 :M f148 sf ( )S 988 0 :M FrMacBegin B 0 FmP F FmOP 254.025 202.5 M -0.013(th element is )W FmE 988 0 :M f203 sf ( )S 990 0 :M FrMacBegin B 0 FmP F FmOP 307.583 202.5 M (C)S FmE 991 0 :M f250 sf ( )S 993 0 :M FrMacBegin B 0 FmP F FmOP 314.253 205 M (i)S FmE 993 0 :M f148 sf ( )S 995 0 :M FrMacBegin B 0 FmP F FmOP 316.476 202.5 M ([)S FmE 995 0 :M f203 sf ( )S 997 0 :M FrMacBegin B 0 FmP F FmOP 319.803 202.5 M (j)S FmE 998 0 :M f148 sf ( )S 1000 0 :M FrMacBegin B 0 FmP F FmOP 322.582 202.5 M -0.013(] and contains )W FmE 1000 0 :M f203 sf ( )S 1002 0 :M FrMacBegin B 0 FmP F FmOP 381.132 202.5 M (P)S FmE 1003 0 :M f250 sf ( )S 1005 0 :M FrMacBegin B 0 FmP F FmOP 387.241 205 M (i)S FmE 1005 0 :M f148 sf ( )S 1007 0 :M FrMacBegin B 0 FmP F FmOP 389.463 202.5 M (\325)S -0.552 N -0.013(s latest v)W -0.251 N -0.013(alue for the current time )W 76 216.333 M (in process )S FmE 1007 0 :M f203 sf ( )S 1009 0 :M FrMacBegin B 0 FmP F FmOP 118.761 216.333 M (P)S FmE 1010 0 :M f250 sf ( )S 1012 0 :M FrMacBegin B 0 FmP F FmOP 124.87 218.833 M (k)S FmE 1012 0 :M f148 sf ( )S 1014 0 :M FrMacBegin B 0 FmP F FmOP 128.42 216.333 M (.)S FmE 1014 0 :M f263 sf ( )S 1017 0 :M FrMacBegin B 0 FmP F FmOP 58 243.5 M (Pr)S -0.217 N (otocol)S FmE 1017 0 :M f148 sf ( )S 1019 0 :M FrMacBegin B 0 FmP F FmOP 58 259.166 M (1.)S 10.5 N (Increment clock )S FmE 1020 0 :M f203 sf ( )S 1022 0 :M FrMacBegin B 0 FmP F FmOP 143.183 259.166 M (C)S FmE 1022 0 :M f250 sf ( )S 1024 0 :M FrMacBegin B 0 FmP F FmOP 149.853 261.666 M (i)S FmE 1024 0 :M f148 sf ( )S 1026 0 :M FrMacBegin B 0 FmP F FmOP 152.075 259.166 M ( between an)S -0.151 N (y tw)S -0.1 N (o successi)S -0.251 N (v)S -0.151 N (e e)S -0.251 N (v)S -0.151 N (ents in process )S FmE 1027 0 :M f203 sf ( )S 1029 0 :M FrMacBegin B 0 FmP F FmOP 339.272 259.166 M (P)S FmE 1029 0 :M f250 sf ( )S 1031 0 :M FrMacBegin B 0 FmP F FmOP 345.381 261.666 M (i)S FmE 1031 0 :M f148 sf ( )S 1033 0 :M FrMacBegin B 0 FmP F FmOP 347.604 259.166 M (: )S FmE 1034 0 :M f203 sf ( )S 1036 0 :M FrMacBegin B 0 FmP F FmOP 352.882 259.166 M (C)S FmE 1036 0 :M f250 sf ( )S 1038 0 :M FrMacBegin B 0 FmP F FmOP 359.552 261.666 M (i)S FmE 1038 0 :M f148 sf ( )S 1040 0 :M FrMacBegin B 0 FmP F FmOP 361.774 259.166 M ([)S FmE 1041 0 :M f203 sf ( )S 1043 0 :M FrMacBegin B 0 FmP F FmOP 365.102 259.166 M (i)S FmE 1043 0 :M f148 sf ( )S 1045 0 :M FrMacBegin B 0 FmP F FmOP 367.88 259.166 M (] )S FmE 1046 0 :M f237 sf ( )S 1048 0 :M FrMacBegin B 0 FmP F FmOP 373.708 259.166 M (\254)S FmE 1048 0 :M f148 sf ( )S 1050 0 :M FrMacBegin B 0 FmP F FmOP 383.576 259.166 M ( )S FmE 1051 0 :M f203 sf ( )S 1053 0 :M FrMacBegin B 0 FmP F FmOP 386.076 259.166 M (C)S FmE 1053 0 :M f250 sf ( )S 1055 0 :M FrMacBegin B 0 FmP F FmOP 392.746 261.666 M (i)S FmE 1055 0 :M f148 sf ( )S 1057 0 :M FrMacBegin B 0 FmP F FmOP 394.969 259.166 M ([)S FmE 1058 0 :M f203 sf ( )S 1060 0 :M FrMacBegin B 0 FmP F FmOP 398.296 259.166 M (i)S FmE 1060 0 :M f148 sf ( )S 1062 0 :M FrMacBegin B 0 FmP F FmOP 401.075 259.166 M (] + )S FmE 1063 0 :M f203 sf ( )S 1065 0 :M FrMacBegin B 0 FmP F FmOP 415.042 259.166 M (d)S FmE 1065 0 :M f148 sf ( )S 1067 0 :M FrMacBegin B 0 FmP F FmOP 420.042 259.166 M ( \()S FmE 1068 0 :M f203 sf ( )S 1070 0 :M FrMacBegin B 0 FmP F FmOP 425.87 259.166 M (d)S FmE 1070 0 :M f148 sf ( )S 1072 0 :M FrMacBegin B 0 FmP F FmOP 430.87 259.166 M ( > 0\))S 58 275.966 M (2.)S 10.5 N (Let e)S -0.251 N (v)S -0.151 N (ent )S FmE 1073 0 :M f203 sf ( )S 1075 0 :M FrMacBegin B 0 FmP F FmOP 115.578 275.966 M (a)S FmE 1075 0 :M f148 sf ( )S 1077 0 :M FrMacBegin B 0 FmP F FmOP 120.578 275.966 M ( be the sending of a message by process )S FmE 1078 0 :M f203 sf ( )S 1080 0 :M FrMacBegin B 0 FmP F FmOP 282.46 275.966 M (P)S FmE 1080 0 :M f250 sf ( )S 1082 0 :M FrMacBegin B 0 FmP F FmOP 288.568 278.466 M (i)S FmE 1082 0 :M f148 sf ( )S 1084 0 :M FrMacBegin B 0 FmP F FmOP 290.791 275.966 M (; its v)S -0.151 N (ector timestamp is )S FmE 1085 0 :M f203 sf ( )S 1087 0 :M FrMacBegin B 0 FmP F FmOP 388.672 275.966 M (t)S FmE 1087 0 :M f250 sf ( )S 1089 0 :M FrMacBegin B 0 FmP F FmOP 391.45 271.966 M (a)S FmE 1089 0 :M f148 sf ( )S 1091 0 :M FrMacBegin B 0 FmP F FmOP 395.45 275.966 M ( = )S FmE 1092 0 :M f203 sf ( )S 1094 0 :M FrMacBegin B 0 FmP F FmOP 406.09 275.966 M (C)S FmE 1094 0 :M f250 sf ( )S 1096 0 :M FrMacBegin B 0 FmP F FmOP 412.76 278.466 M (i)S FmE 1096 0 :M f148 sf ( )S 1098 0 :M FrMacBegin B 0 FmP F FmOP 414.982 275.966 M (\()S FmE 1099 0 :M f203 sf ( )S 1101 0 :M FrMacBegin B 0 FmP F FmOP 418.31 275.966 M (a)S FmE 1101 0 :M f148 sf ( )S 1103 0 :M FrMacBegin B 0 FmP F FmOP 423.31 275.966 M (\) )S FmE 1104 0 :M f203 sf ( )S 1106 0 :M FrMacBegin B 0 FmP F FmOP 429.138 275.966 M (after)S FmE 1106 0 :M f148 sf ( )S 1108 0 :M FrMacBegin B 0 FmP F FmOP 448.022 275.966 M ( the clock is incre-)S 76 289.8 M (mented.. Let )S FmE 1109 0 :M f203 sf ( )S 1111 0 :M FrMacBegin B 0 FmP F FmOP 128.759 289.8 M (b)S FmE 1111 0 :M f148 sf ( )S 1113 0 :M FrMacBegin B 0 FmP F FmOP 133.759 289.8 M ( be the receipt of that message by )S FmE 1114 0 :M f203 sf ( )S 1116 0 :M FrMacBegin B 0 FmP F FmOP 269.809 289.8 M (P)S FmE 1116 0 :M f250 sf ( )S 1118 0 :M FrMacBegin B 0 FmP F FmOP 275.917 292.3 M (j)S FmE 1118 0 :M f148 sf ( )S 1120 0 :M FrMacBegin B 0 FmP F FmOP 278.14 289.8 M (. )S -0.181 N (Then when )S FmE 1121 0 :M f203 sf ( )S 1123 0 :M FrMacBegin B 0 FmP F FmOP 330.164 289.8 M (P)S FmE 1123 0 :M f250 sf ( )S 1125 0 :M FrMacBegin B 0 FmP F FmOP 336.272 292.3 M (j)S FmE 1125 0 :M f148 sf ( )S 1127 0 :M FrMacBegin B 0 FmP F FmOP 338.495 289.8 M ( recei)S -0.251 N (v)S -0.151 N (es the message, it updates its v)S -0.151 N (ector )S 76 306.299 M (clock for all )S FmE 1128 0 :M f203 sf ( )S 1130 0 :M FrMacBegin B 0 FmP F FmOP 126.806 306.299 M (k)S FmE 1130 0 :M f148 sf ( )S 1132 0 :M FrMacBegin B 0 FmP F FmOP 131.244 306.299 M ( = 1, \311, )S FmE 1133 0 :M f203 sf ( )S 1135 0 :M FrMacBegin B 0 FmP F FmOP 166.884 306.299 M (n)S FmE 1135 0 :M f148 sf ( )S 1137 0 :M FrMacBegin B 0 FmP F FmOP 171.884 306.299 M (: )S FmE 1138 0 :M f203 sf ( )S 1140 0 :M FrMacBegin B 0 FmP F FmOP 177.162 306.299 M (C)S FmE 1140 0 :M f250 sf ( )S 1142 0 :M FrMacBegin B 0 FmP F FmOP 183.832 308.799 M (j)S FmE 1142 0 :M f148 sf ( )S 1144 0 :M FrMacBegin B 0 FmP F FmOP 186.055 306.299 M ([)S FmE 1145 0 :M f203 sf ( )S 1147 0 :M FrMacBegin B 0 FmP F FmOP 189.382 306.299 M (k)S FmE 1147 0 :M f148 sf ( )S 1149 0 :M FrMacBegin B 0 FmP F FmOP 193.821 306.299 M (] )S FmE 1150 0 :M f237 sf ( )S 1152 0 :M FrMacBegin B 0 FmP F FmOP 199.648 306.299 M (\254)S FmE 1152 0 :M f148 sf ( )S 1154 0 :M FrMacBegin B 0 FmP F FmOP 209.517 306.299 M ( max\()S FmE 1155 0 :M f203 sf ( )S 1157 0 :M FrMacBegin B 0 FmP F FmOP 232.561 306.299 M (C)S FmE 1157 0 :M f250 sf ( )S 1159 0 :M FrMacBegin B 0 FmP F FmOP 239.231 308.799 M (j)S FmE 1159 0 :M f148 sf ( )S 1161 0 :M FrMacBegin B 0 FmP F FmOP 241.454 306.299 M ([)S FmE 1162 0 :M f203 sf ( )S 1164 0 :M FrMacBegin B 0 FmP F FmOP 244.781 306.299 M (k)S FmE 1164 0 :M f148 sf ( )S 1166 0 :M FrMacBegin B 0 FmP F FmOP 249.22 306.299 M (], )S FmE 1167 0 :M f203 sf ( )S 1169 0 :M FrMacBegin B 0 FmP F FmOP 257.547 306.299 M (t)S FmE 1169 0 :M f250 sf ( )S 1171 0 :M FrMacBegin B 0 FmP F FmOP 260.326 302.299 M (a)S FmE 1171 0 :M f148 sf ( )S 1173 0 :M FrMacBegin B 0 FmP F FmOP 264.326 306.299 M ([)S FmE 1174 0 :M f203 sf ( )S 1176 0 :M FrMacBegin B 0 FmP F FmOP 267.653 306.299 M (k)S FmE 1176 0 :M f148 sf ( )S 1178 0 :M FrMacBegin B 0 FmP F FmOP 272.092 306.299 M (]\))S FmE 1179 0 :M f263 sf ( )S 1182 0 :M FrMacBegin B 0 FmP F FmOP 58 333.466 M (Example)S FmE 1182 0 :M f148 sf ( )S 1184 0 :M FrMacBegin B 0 FmP F FmOP 58 471.133 M (Here is the progression of time for the three processes:)S FmE 1184 0 :M f203 sf ( )S 1186 0 :M FrMacBegin B 0 FmP F FmOP 58 483.133 M (e)S FmE 1187 0 :M f276 sf ( )S 1189 0 :M FrMacBegin B 0 FmP F FmOP 62.438 485.633 M (11)S FmE 1189 0 :M f148 sf ( )S 1191 0 :M FrMacBegin B 0 FmP F FmOP 70.438 483.133 M (: )S FmE 1191 0 :M f203 sf ( )S 1193 0 :M FrMacBegin B 0 FmP F FmOP 75.717 483.133 M (C)S FmE 1194 0 :M f276 sf ( )S 1196 0 :M FrMacBegin B 0 FmP F FmOP 82.387 485.633 M (1)S FmE 1196 0 :M f148 sf ( )S 1198 0 :M FrMacBegin B 0 FmP F FmOP 86.387 483.133 M ( )S FmE 1198 0 :M f237 sf ( )S 1200 0 :M FrMacBegin B 0 FmP F FmOP 88.887 483.133 M (\254)S FmE 1201 0 :M f148 sf ( )S 1203 0 :M FrMacBegin B 0 FmP F FmOP 98.755 483.133 M ( \(1, 0, 0\))S FmE 1203 0 :M f203 sf ( )S 1205 0 :M FrMacBegin B 0 FmP F FmOP 58 499.632 M (e)S FmE 1206 0 :M f276 sf ( )S 1208 0 :M FrMacBegin B 0 FmP F FmOP 62.438 502.132 M (31)S FmE 1208 0 :M f148 sf ( )S 1210 0 :M FrMacBegin B 0 FmP F FmOP 70.438 499.632 M (: )S FmE 1210 0 :M f203 sf ( )S 1212 0 :M FrMacBegin B 0 FmP F FmOP 75.717 499.632 M (C)S FmE 1213 0 :M f276 sf ( )S 1215 0 :M FrMacBegin B 0 FmP F FmOP 82.387 502.132 M (3)S FmE 1215 0 :M f148 sf ( )S 1217 0 :M FrMacBegin B 0 FmP F FmOP 86.387 499.632 M ( )S FmE 1217 0 :M f237 sf ( )S 1219 0 :M FrMacBegin B 0 FmP F FmOP 88.887 499.632 M (\254)S FmE 1220 0 :M f148 sf ( )S 1222 0 :M FrMacBegin B 0 FmP F FmOP 98.755 499.632 M ( \(0, 0, 1\); timestamp )S FmE 1222 0 :M f203 sf ( )S 1224 0 :M FrMacBegin B 0 FmP F FmOP 182.346 499.632 M (t)S FmE 1225 0 :M f276 sf ( )S 1227 0 :M FrMacBegin B 0 FmP F FmOP 185.125 495.633 M (3,1)S FmE 1227 0 :M f203 sf ( )S 1229 0 :M FrMacBegin B 0 FmP F FmOP 195.125 499.632 M ( )S FmE 1229 0 :M f148 sf ( )S 1231 0 :M FrMacBegin B 0 FmP F FmOP 197.625 499.632 M (of message is \(0, 0, 1\))S FmE 1232 0 :M f203 sf ( )S 1234 0 :M FrMacBegin B 0 FmP F FmOP 58 516.132 M (e)S FmE 1234 0 :M f276 sf ( )S 1236 0 :M FrMacBegin B 0 FmP F FmOP 62.438 518.632 M (21)S FmE 1236 0 :M f148 sf ( )S 1238 0 :M FrMacBegin B 0 FmP F FmOP 70.438 516.132 M -0.2(: )W FmE 1239 0 :M f203 sf ( )S 1241 0 :M FrMacBegin B 0 FmP F FmOP 75.517 516.132 M (C)S FmE 1241 0 :M f276 sf ( )S 1243 0 :M FrMacBegin B 0 FmP F FmOP 82.187 518.632 M (2)S FmE 1243 0 :M f148 sf ( )S 1245 0 :M FrMacBegin B 0 FmP F FmOP 86.187 516.132 M -0.2( )W FmE 1246 0 :M f237 sf ( )S 1248 0 :M FrMacBegin B 0 FmP F FmOP 88.488 516.132 M (\254)S FmE 1248 0 :M f148 sf ( )S 1250 0 :M FrMacBegin B 0 FmP F FmOP 98.356 516.132 M -0.2( \(0, 1, 1\) as )W FmE 1251 0 :M f203 sf ( )S 1253 0 :M FrMacBegin B 0 FmP F FmOP 147.141 516.132 M (t)S FmE 1253 0 :M f276 sf ( )S 1255 0 :M FrMacBegin B 0 FmP F FmOP 149.919 512.132 M (3,1)S FmE 1255 0 :M f148 sf ( )S 1257 0 :M FrMacBegin B 0 FmP F FmOP 159.919 516.132 M -0.2( = \(0, 0, 1\), )W FmE 1258 0 :M f203 sf ( )S 1260 0 :M FrMacBegin B 0 FmP F FmOP 208.517 516.132 M (C)S FmE 1260 0 :M f276 sf ( )S 1262 0 :M FrMacBegin B 0 FmP F FmOP 215.187 518.632 M (2)S FmE 1262 0 :M f148 sf ( )S 1264 0 :M FrMacBegin B 0 FmP F FmOP 219.187 516.132 M -0.2( )W FmE 1265 0 :M f237 sf ( )S 1267 0 :M FrMacBegin B 0 FmP F FmOP 221.487 516.132 M (\254)S FmE 1267 0 :M f148 sf ( )S 1269 0 :M FrMacBegin B 0 FmP F FmOP 231.355 516.132 M -0.2( \(0, 1, 0\) after the increment, )W FmE 1270 0 :M f203 sf ( )S 1272 0 :M FrMacBegin B 0 FmP F FmOP 347.119 516.132 M (C)S FmE 1272 0 :M f276 sf ( )S 1274 0 :M FrMacBegin B 0 FmP F FmOP 353.789 518.632 M (2)S FmE 1274 0 :M f148 sf ( )S 1276 0 :M FrMacBegin B 0 FmP F FmOP 357.789 516.132 M -0.2([0] )W FmE 1277 0 :M f237 sf ( )S 1279 0 :M FrMacBegin B 0 FmP F FmOP 371.745 516.132 M (\254)S FmE 1279 0 :M f148 sf ( )S 1281 0 :M FrMacBegin B 0 FmP F FmOP 381.613 516.132 M -0.2( max\()W FmE 1282 0 :M f203 sf ( )S 1284 0 :M FrMacBegin B 0 FmP F FmOP 404.458 516.132 M (C)S FmE 1284 0 :M f276 sf ( )S 1286 0 :M FrMacBegin B 0 FmP F FmOP 411.127 518.632 M (2)S FmE 1286 0 :M f148 sf ( )S 1288 0 :M FrMacBegin B 0 FmP F FmOP 415.127 516.132 M -0.2([0], )W FmE 1289 0 :M f203 sf ( )S 1291 0 :M FrMacBegin B 0 FmP F FmOP 431.583 516.132 M (t)S FmE 1291 0 :M f276 sf ( )S 1293 0 :M FrMacBegin B 0 FmP F FmOP 434.361 512.132 M (3,1)S FmE 1293 0 :M f148 sf ( )S 1295 0 :M FrMacBegin B 0 FmP F FmOP 444.361 516.132 M -0.2([0]\) = max\(0, 0\) = 0,)W FmE 1296 0 :M f203 sf ( )S 1298 0 :M FrMacBegin B 0 FmP F FmOP 76 532.632 M (C)S FmE 1298 0 :M f276 sf ( )S 1300 0 :M FrMacBegin B 0 FmP F FmOP 82.67 535.132 M (2)S FmE 1300 0 :M f148 sf ( )S 1302 0 :M FrMacBegin B 0 FmP F FmOP 86.67 532.632 M ([1] )S FmE 1303 0 :M f237 sf ( )S 1305 0 :M FrMacBegin B 0 FmP F FmOP 100.825 532.632 M (\254)S FmE 1305 0 :M f148 sf ( )S 1307 0 :M FrMacBegin B 0 FmP F FmOP 110.693 532.632 M ( max\()S FmE 1308 0 :M f203 sf ( )S 1310 0 :M FrMacBegin B 0 FmP F FmOP 133.738 532.632 M (C)S FmE 1310 0 :M f276 sf ( )S 1312 0 :M FrMacBegin B 0 FmP F FmOP 140.408 535.132 M (2)S FmE 1312 0 :M f148 sf ( )S 1314 0 :M FrMacBegin B 0 FmP F FmOP 144.408 532.632 M ([1], )S FmE 1315 0 :M f203 sf ( )S 1317 0 :M FrMacBegin B 0 FmP F FmOP 161.063 532.632 M (t)S FmE 1317 0 :M f276 sf ( )S 1319 0 :M FrMacBegin B 0 FmP F FmOP 163.841 528.632 M (3,1)S FmE 1319 0 :M f148 sf ( )S 1321 0 :M FrMacBegin B 0 FmP F FmOP 173.841 532.632 M ([1]\) = max\(1, 0\) = 1, and )S FmE 1322 0 :M f203 sf ( )S 1324 0 :M FrMacBegin B 0 FmP F FmOP 275.914 532.632 M (C)S FmE 1324 0 :M f276 sf ( )S 1326 0 :M FrMacBegin B 0 FmP F FmOP 282.584 535.132 M (2)S FmE 1326 0 :M f148 sf ( )S 1328 0 :M FrMacBegin B 0 FmP F FmOP 286.584 532.632 M ([2] )S FmE 1329 0 :M f237 sf ( )S 1331 0 :M FrMacBegin B 0 FmP F FmOP 300.739 532.632 M (\254)S FmE 1331 0 :M f148 sf ( )S 1333 0 :M FrMacBegin B 0 FmP F FmOP 310.607 532.632 M ( max\()S FmE 1334 0 :M f203 sf ( )S 1336 0 :M FrMacBegin B 0 FmP F FmOP 333.652 532.632 M (C)S FmE 1336 0 :M f276 sf ( )S 1338 0 :M FrMacBegin B 0 FmP F FmOP 340.322 535.132 M (2)S FmE 1338 0 :M f148 sf ( )S 1340 0 :M FrMacBegin B 0 FmP F FmOP 344.322 532.632 M ([2], )S FmE 1341 0 :M f203 sf ( )S 1343 0 :M FrMacBegin B 0 FmP F FmOP 360.977 532.632 M (t)S FmE 1343 0 :M f276 sf ( )S 1345 0 :M FrMacBegin B 0 FmP F FmOP 363.755 528.632 M (3,1)S FmE 1345 0 :M f148 sf ( )S 1347 0 :M FrMacBegin B 0 FmP F FmOP 373.755 532.632 M ([2]\) = max\(0, 1\) = 1)S FmE 1348 0 :M f203 sf ( )S 1350 0 :M FrMacBegin B 0 FmP F FmOP 58 549.132 M (e)S FmE 1350 0 :M f276 sf ( )S 1352 0 :M FrMacBegin B 0 FmP F FmOP 62.438 551.632 M (22)S FmE 1352 0 :M f148 sf ( )S 1354 0 :M FrMacBegin B 0 FmP F FmOP 70.438 549.132 M (: )S FmE 1355 0 :M f203 sf ( )S 1357 0 :M FrMacBegin B 0 FmP F FmOP 75.717 549.132 M (C)S FmE 1357 0 :M f276 sf ( )S 1359 0 :M FrMacBegin B 0 FmP F FmOP 82.387 551.632 M (2)S FmE 1359 0 :M f148 sf ( )S 1361 0 :M FrMacBegin B 0 FmP F FmOP 86.387 549.132 M ( )S FmE 1362 0 :M f237 sf ( )S 1364 0 :M FrMacBegin B 0 FmP F FmOP 88.887 549.132 M (\254)S FmE 1364 0 :M f148 sf ( )S 1366 0 :M FrMacBegin B 0 FmP F FmOP 98.755 549.132 M ( \(0, 2, 1\); timestamp )S FmE 1367 0 :M f203 sf ( )S 1369 0 :M FrMacBegin B 0 FmP F FmOP 182.346 549.132 M (t)S FmE 1369 0 :M f276 sf ( )S 1371 0 :M FrMacBegin B 0 FmP F FmOP 185.125 545.132 M (2,1)S FmE 1371 0 :M f203 sf ( )S 1373 0 :M FrMacBegin B 0 FmP F FmOP 195.125 549.132 M ( )S FmE 1374 0 :M f148 sf ( )S 1376 0 :M FrMacBegin B 0 FmP F FmOP 197.625 549.132 M (of message is \(0, 2, 1\))S FmE 1376 0 :M f203 sf ( )S 1378 0 :M FrMacBegin B 0 FmP F FmOP 58 565.632 M (e)S FmE 1379 0 :M f276 sf ( )S 1381 0 :M FrMacBegin B 0 FmP F FmOP 62.438 568.132 M (12)S FmE 1381 0 :M f148 sf ( )S 1383 0 :M FrMacBegin B 0 FmP F FmOP 70.438 565.632 M (: )S FmE 1383 0 :M f203 sf ( )S 1385 0 :M FrMacBegin B 0 FmP F FmOP 75.717 565.632 M (C)S FmE 1386 0 :M f276 sf ( )S 1388 0 :M FrMacBegin B 0 FmP F FmOP 82.387 568.132 M (1)S FmE 1388 0 :M f148 sf ( )S 1390 0 :M FrMacBegin B 0 FmP F FmOP 86.387 565.632 M ( )S FmE 1390 0 :M f237 sf ( )S 1392 0 :M FrMacBegin B 0 FmP F FmOP 88.887 565.632 M (\254)S FmE 1393 0 :M f148 sf ( )S 1395 0 :M FrMacBegin B 0 FmP F FmOP 98.755 565.632 M ( \(2, 0, 0\); timestamp )S FmE 1395 0 :M f203 sf ( )S 1397 0 :M FrMacBegin B 0 FmP F FmOP 182.346 565.632 M (t)S FmE 1398 0 :M f276 sf ( )S 1400 0 :M FrMacBegin B 0 FmP F FmOP 185.125 561.632 M (1,1)S FmE 1400 0 :M f203 sf ( )S 1402 0 :M FrMacBegin B 0 FmP F FmOP 195.125 565.632 M ( )S FmE 1402 0 :M f148 sf ( )S 1404 0 :M FrMacBegin B 0 FmP F FmOP 197.625 565.632 M (of message is \(2, 0, 0\))S FmE 1405 0 :M f203 sf ( )S 1407 0 :M FrMacBegin B 0 FmP F FmOP 58 582.132 M (e)S FmE 1407 0 :M f276 sf ( )S 1409 0 :M FrMacBegin B 0 FmP F FmOP 62.438 584.632 M (23)S FmE 1409 0 :M f148 sf ( )S 1411 0 :M FrMacBegin B 0 FmP F FmOP 70.438 582.132 M -0.12(: )W FmE 1412 0 :M f203 sf ( )S 1414 0 :M FrMacBegin B 0 FmP F FmOP 75.597 582.132 M (C)S FmE 1414 0 :M f276 sf ( )S 1416 0 :M FrMacBegin B 0 FmP F FmOP 82.266 584.632 M (2)S FmE 1416 0 :M f148 sf ( )S 1418 0 :M FrMacBegin B 0 FmP F FmOP 86.266 582.132 M -0.12( )W FmE 1419 0 :M f237 sf ( )S 1421 0 :M FrMacBegin B 0 FmP F FmOP 88.646 582.132 M (\254)S FmE 1421 0 :M f148 sf ( )S 1423 0 :M FrMacBegin B 0 FmP F FmOP 98.514 582.132 M -0.12( \(2, 3, 1\) as )W FmE 1424 0 :M f203 sf ( )S 1426 0 :M FrMacBegin B 0 FmP F FmOP 145.396 582.132 M (t)S FmE 1426 0 :M f276 sf ( )S 1428 0 :M FrMacBegin B 0 FmP F FmOP 148.174 578.132 M (1,1)S FmE 1428 0 :M f148 sf ( )S 1430 0 :M FrMacBegin B 0 FmP F FmOP 158.174 582.132 M -0.12( = \(2, 0, 0\), )W FmE 1431 0 :M f203 sf ( )S 1433 0 :M FrMacBegin B 0 FmP F FmOP 207.248 582.132 M (C)S FmE 1433 0 :M f276 sf ( )S 1435 0 :M FrMacBegin B 0 FmP F FmOP 213.918 584.632 M (2)S FmE 1435 0 :M f148 sf ( )S 1437 0 :M FrMacBegin B 0 FmP F FmOP 217.918 582.132 M -0.12( )W FmE 1438 0 :M f237 sf ( )S 1440 0 :M FrMacBegin B 0 FmP F FmOP 220.298 582.132 M (\254)S FmE 1440 0 :M f148 sf ( )S 1442 0 :M FrMacBegin B 0 FmP F FmOP 230.166 582.132 M -0.12( \(0, 3, 1\) after the increment, )W FmE 1443 0 :M f203 sf ( )S 1445 0 :M FrMacBegin B 0 FmP F FmOP 346.485 582.132 M (C)S FmE 1445 0 :M f276 sf ( )S 1447 0 :M FrMacBegin B 0 FmP F FmOP 353.155 584.632 M (2)S FmE 1447 0 :M f148 sf ( )S 1449 0 :M FrMacBegin B 0 FmP F FmOP 357.155 582.132 M -0.12([0] )W FmE 1450 0 :M f237 sf ( )S 1452 0 :M FrMacBegin B 0 FmP F FmOP 371.19 582.132 M (\254)S FmE 1452 0 :M f148 sf ( )S 1454 0 :M FrMacBegin B 0 FmP F FmOP 381.058 582.132 M -0.12( max\()W FmE 1455 0 :M f203 sf ( )S 1457 0 :M FrMacBegin B 0 FmP F FmOP 403.982 582.132 M (C)S FmE 1457 0 :M f276 sf ( )S 1459 0 :M FrMacBegin B 0 FmP F FmOP 410.652 584.632 M (2)S FmE 1459 0 :M f148 sf ( )S 1461 0 :M FrMacBegin B 0 FmP F FmOP 414.652 582.132 M -0.12([0], )W FmE 1462 0 :M f203 sf ( )S 1464 0 :M FrMacBegin B 0 FmP F FmOP 431.187 582.132 M (t)S FmE 1464 0 :M f276 sf ( )S 1466 0 :M FrMacBegin B 0 FmP F FmOP 433.965 578.132 M (1,1)S FmE 1466 0 :M f148 sf ( )S 1468 0 :M FrMacBegin B 0 FmP F FmOP 443.965 582.132 M -0.12([0]\) = max\(0, 2\) = 2,)W FmE 1469 0 :M f203 sf ( )S 1471 0 :M FrMacBegin B 0 FmP F FmOP 76 598.631 M (C)S FmE 1471 0 :M f276 sf ( )S 1473 0 :M FrMacBegin B 0 FmP F FmOP 82.67 601.131 M (2)S FmE 1473 0 :M f148 sf ( )S 1475 0 :M FrMacBegin B 0 FmP F FmOP 86.67 598.631 M ([1] )S FmE 1476 0 :M f237 sf ( )S 1478 0 :M FrMacBegin B 0 FmP F FmOP 100.825 598.631 M (\254)S FmE 1478 0 :M f148 sf ( )S 1480 0 :M FrMacBegin B 0 FmP F FmOP 110.693 598.631 M ( max\()S FmE 1481 0 :M f203 sf ( )S 1483 0 :M FrMacBegin B 0 FmP F FmOP 133.738 598.631 M (C)S FmE 1483 0 :M f276 sf ( )S 1485 0 :M FrMacBegin B 0 FmP F FmOP 140.408 601.131 M (2)S FmE 1485 0 :M f148 sf ( )S 1487 0 :M FrMacBegin B 0 FmP F FmOP 144.408 598.631 M ([1], )S FmE 1488 0 :M f203 sf ( )S 1490 0 :M FrMacBegin B 0 FmP F FmOP 161.063 598.631 M (t)S FmE 1490 0 :M f276 sf ( )S 1492 0 :M FrMacBegin B 0 FmP F FmOP 163.841 594.631 M (1,1)S FmE 1492 0 :M f148 sf ( )S 1494 0 :M FrMacBegin B 0 FmP F FmOP 173.841 598.631 M ([1]\) = max\(3, 0\) = 3, and )S FmE 1495 0 :M f203 sf ( )S 1497 0 :M FrMacBegin B 0 FmP F FmOP 275.914 598.631 M (C)S FmE 1497 0 :M f276 sf ( )S 1499 0 :M FrMacBegin B 0 FmP F FmOP 282.584 601.131 M (2)S FmE 1499 0 :M f148 sf ( )S 1501 0 :M FrMacBegin B 0 FmP F FmOP 286.584 598.631 M ([2] )S FmE 1502 0 :M f237 sf ( )S 1504 0 :M FrMacBegin B 0 FmP F FmOP 300.739 598.631 M (\254)S FmE 1504 0 :M f148 sf ( )S 1506 0 :M FrMacBegin B 0 FmP F FmOP 310.607 598.631 M ( max\()S FmE 1507 0 :M f203 sf ( )S 1509 0 :M FrMacBegin B 0 FmP F FmOP 333.652 598.631 M (C)S FmE 1509 0 :M f276 sf ( )S 1511 0 :M FrMacBegin B 0 FmP F FmOP 340.322 601.131 M (2)S FmE 1511 0 :M f148 sf ( )S 1513 0 :M FrMacBegin B 0 FmP F FmOP 344.322 598.631 M ([2], )S FmE 1514 0 :M f203 sf ( )S 1516 0 :M FrMacBegin B 0 FmP F FmOP 360.977 598.631 M (t)S FmE 1516 0 :M f276 sf ( )S 1518 0 :M FrMacBegin B 0 FmP F FmOP 363.755 594.631 M (1,1)S FmE 1518 0 :M f148 sf ( )S 1520 0 :M FrMacBegin B 0 FmP F FmOP 373.755 598.631 M ([2]\) = max\(0, 1\) = 1)S FmE 1521 0 :M f203 sf ( )S 1523 0 :M FrMacBegin B 0 FmP F FmOP 58 615.131 M (e)S FmE 1523 0 :M f276 sf ( )S 1525 0 :M FrMacBegin B 0 FmP F FmOP 62.438 617.631 M (24)S FmE 1525 0 :M f148 sf ( )S 1527 0 :M FrMacBegin B 0 FmP F FmOP 70.438 615.131 M (: )S FmE 1528 0 :M f203 sf ( )S 1530 0 :M FrMacBegin B 0 FmP F FmOP 75.717 615.131 M (C)S FmE 1530 0 :M f276 sf ( )S 1532 0 :M FrMacBegin B 0 FmP F FmOP 82.387 617.631 M (2)S FmE 1532 0 :M f148 sf ( )S 1534 0 :M FrMacBegin B 0 FmP F FmOP 86.387 615.131 M ( )S FmE 1535 0 :M f237 sf ( )S 1537 0 :M FrMacBegin B 0 FmP F FmOP 88.887 615.131 M (\254)S FmE 1537 0 :M f148 sf ( )S 1539 0 :M FrMacBegin B 0 FmP F FmOP 98.755 615.131 M ( \(2, 3, 1\); timestamp )S FmE 1540 0 :M f203 sf ( )S 1542 0 :M FrMacBegin B 0 FmP F FmOP 182.346 615.131 M (t)S FmE 1542 0 :M f276 sf ( )S 1544 0 :M FrMacBegin B 0 FmP F FmOP 185.125 611.131 M (2,2)S FmE 1544 0 :M f203 sf ( )S 1546 0 :M FrMacBegin B 0 FmP F FmOP 195.125 615.131 M ( )S FmE 1547 0 :M f148 sf ( )S 1549 0 :M FrMacBegin B 0 FmP F FmOP 197.625 615.131 M (of message is \(2, 3, 1\))S FmE 1549 0 :M f203 sf ( )S 1551 0 :M FrMacBegin B 0 FmP F FmOP 58 631.631 M (e)S FmE 1552 0 :M f276 sf ( )S 1554 0 :M FrMacBegin B 0 FmP F FmOP 62.438 634.131 M (13)S FmE 1554 0 :M f148 sf ( )S 1556 0 :M FrMacBegin B 0 FmP F FmOP 70.438 631.631 M -0.12(: )W FmE 1556 0 :M f203 sf ( )S 1558 0 :M FrMacBegin B 0 FmP F FmOP 75.597 631.631 M (C)S FmE 1559 0 :M f276 sf ( )S 1561 0 :M FrMacBegin B 0 FmP F FmOP 82.266 634.131 M (1)S FmE 1561 0 :M f148 sf ( )S 1563 0 :M FrMacBegin B 0 FmP F FmOP 86.266 631.631 M -0.12( )W FmE 1563 0 :M f237 sf ( )S 1565 0 :M FrMacBegin B 0 FmP F FmOP 88.646 631.631 M (\254)S FmE 1566 0 :M f148 sf ( )S 1568 0 :M FrMacBegin B 0 FmP F FmOP 98.514 631.631 M -0.12( \(3, 2, 1\) as )W FmE 1568 0 :M f203 sf ( )S 1570 0 :M FrMacBegin B 0 FmP F FmOP 145.396 631.631 M (t)S FmE 1571 0 :M f276 sf ( )S 1573 0 :M FrMacBegin B 0 FmP F FmOP 148.174 627.631 M (2,1)S FmE 1573 0 :M f148 sf ( )S 1575 0 :M FrMacBegin B 0 FmP F FmOP 158.174 631.631 M -0.12( = \(0, 2, 1\), )W FmE 1575 0 :M f203 sf ( )S 1577 0 :M FrMacBegin B 0 FmP F FmOP 207.248 631.631 M (C)S FmE 1578 0 :M f276 sf ( )S 1580 0 :M FrMacBegin B 0 FmP F FmOP 213.918 634.131 M (1)S FmE 1580 0 :M f148 sf ( )S 1582 0 :M FrMacBegin B 0 FmP F FmOP 217.918 631.631 M -0.12( )W FmE 1582 0 :M f237 sf ( )S 1584 0 :M FrMacBegin B 0 FmP F FmOP 220.298 631.631 M (\254)S FmE 1585 0 :M f148 sf ( )S 1587 0 :M FrMacBegin B 0 FmP F FmOP 230.166 631.631 M -0.12( \(3, 0, 0\) after the increment, )W FmE 1587 0 :M f203 sf ( )S 1589 0 :M FrMacBegin B 0 FmP F FmOP 346.485 631.631 M (C)S FmE 1590 0 :M f276 sf ( )S 1592 0 :M FrMacBegin B 0 FmP F FmOP 353.155 634.131 M (1)S FmE 1592 0 :M f148 sf ( )S 1594 0 :M FrMacBegin B 0 FmP F FmOP 357.155 631.631 M -0.12([0] )W FmE 1594 0 :M f237 sf ( )S 1596 0 :M FrMacBegin B 0 FmP F FmOP 371.19 631.631 M (\254)S FmE 1597 0 :M f148 sf ( )S 1599 0 :M FrMacBegin B 0 FmP F FmOP 381.058 631.631 M -0.12( max\()W FmE 1599 0 :M f203 sf ( )S 1601 0 :M FrMacBegin B 0 FmP F FmOP 403.982 631.631 M (C)S FmE 1602 0 :M f276 sf ( )S 1604 0 :M FrMacBegin B 0 FmP F FmOP 410.652 634.131 M (1)S FmE 1604 0 :M f148 sf ( )S 1606 0 :M FrMacBegin B 0 FmP F FmOP 414.652 631.631 M -0.12([0], )W FmE 1606 0 :M f203 sf ( )S 1608 0 :M FrMacBegin B 0 FmP F FmOP 431.187 631.631 M (t)S FmE 1609 0 :M f276 sf ( )S 1611 0 :M FrMacBegin B 0 FmP F FmOP 433.965 627.631 M (2,1)S FmE 1611 0 :M f148 sf ( )S 1613 0 :M FrMacBegin B 0 FmP F FmOP 443.965 631.631 M -0.12([0]\) = max\(3, 0\) = 3,)W FmE 1613 0 :M f203 sf ( )S 1615 0 :M FrMacBegin B 0 FmP F FmOP 76 648.131 M (C)S FmE 1616 0 :M f276 sf ( )S 1618 0 :M FrMacBegin B 0 FmP F FmOP 82.67 650.631 M (1)S FmE 1618 0 :M f148 sf ( )S 1620 0 :M FrMacBegin B 0 FmP F FmOP 86.67 648.131 M ([1] )S FmE 1620 0 :M f237 sf ( )S 1622 0 :M FrMacBegin B 0 FmP F FmOP 100.825 648.131 M (\254)S FmE 1623 0 :M f148 sf ( )S 1625 0 :M FrMacBegin B 0 FmP F FmOP 110.693 648.131 M ( max\()S FmE 1625 0 :M f203 sf ( )S 1627 0 :M FrMacBegin B 0 FmP F FmOP 133.738 648.131 M (C)S FmE 1628 0 :M f276 sf ( )S 1630 0 :M FrMacBegin B 0 FmP F FmOP 140.408 650.631 M (1)S FmE 1630 0 :M f148 sf ( )S 1632 0 :M FrMacBegin B 0 FmP F FmOP 144.408 648.131 M ([1], )S FmE 1632 0 :M f203 sf ( )S 1634 0 :M FrMacBegin B 0 FmP F FmOP 161.063 648.131 M (t)S FmE 1635 0 :M f276 sf ( )S 1637 0 :M FrMacBegin B 0 FmP F FmOP 163.841 644.131 M (2,1)S FmE 1637 0 :M f148 sf ( )S 1639 0 :M FrMacBegin B 0 FmP F FmOP 173.841 648.131 M ([1]\) = max\(2, 0\) = 2, and )S FmE 1639 0 :M f203 sf ( )S 1641 0 :M FrMacBegin B 0 FmP F FmOP 275.914 648.131 M (C)S FmE 1642 0 :M f276 sf ( )S 1644 0 :M FrMacBegin B 0 FmP F FmOP 282.584 650.631 M (1)S FmE 1644 0 :M f148 sf ( )S 1646 0 :M FrMacBegin B 0 FmP F FmOP 286.584 648.131 M ([2] )S FmE 1646 0 :M f237 sf ( )S 1648 0 :M FrMacBegin B 0 FmP F FmOP 300.739 648.131 M (\254)S FmE 1649 0 :M f148 sf ( )S 1651 0 :M FrMacBegin B 0 FmP F FmOP 310.607 648.131 M ( max\()S FmE 1651 0 :M f203 sf ( )S 1653 0 :M FrMacBegin B 0 FmP F FmOP 333.652 648.131 M (C)S FmE 1654 0 :M f276 sf ( )S 1656 0 :M FrMacBegin B 0 FmP F FmOP 340.322 650.631 M (1)S FmE 1656 0 :M f148 sf ( )S 1658 0 :M FrMacBegin B 0 FmP F FmOP 344.322 648.131 M ([2], )S FmE 1658 0 :M f203 sf ( )S 1660 0 :M FrMacBegin B 0 FmP F FmOP 360.977 648.131 M (t)S FmE 1661 0 :M f276 sf ( )S 1663 0 :M FrMacBegin B 0 FmP F FmOP 363.755 644.131 M (2,1)S FmE 1663 0 :M f148 sf ( )S 1665 0 :M FrMacBegin B 0 FmP F FmOP 373.755 648.131 M ([2]\) = max\(1, 0\) = 1)S FmE 1665 0 :M f203 sf ( )S 1667 0 :M FrMacBegin B 0 FmP F FmOP 58 664.631 M (e)S FmE 1668 0 :M f276 sf ( )S 1670 0 :M FrMacBegin B 0 FmP F FmOP 62.438 667.131 M (32)S FmE 1670 0 :M f148 sf ( )S 1672 0 :M FrMacBegin B 0 FmP F FmOP 70.438 664.631 M -0.12(: )W FmE 1672 0 :M f203 sf ( )S 1674 0 :M FrMacBegin B 0 FmP F FmOP 75.597 664.631 M (C)S FmE 1675 0 :M f276 sf ( )S 1677 0 :M FrMacBegin B 0 FmP F FmOP 82.266 667.131 M (3)S FmE 1677 0 :M f148 sf ( )S 1679 0 :M FrMacBegin B 0 FmP F FmOP 86.266 664.631 M -0.12( )W FmE 1679 0 :M f237 sf ( )S 1681 0 :M FrMacBegin B 0 FmP F FmOP 88.646 664.631 M (\254)S FmE 1682 0 :M f148 sf ( )S 1684 0 :M FrMacBegin B 0 FmP F FmOP 98.514 664.631 M -0.12( \(2, 3, 2\) as )W FmE 1684 0 :M f203 sf ( )S 1686 0 :M FrMacBegin B 0 FmP F FmOP 145.396 664.631 M (t)S FmE 1687 0 :M f276 sf ( )S 1689 0 :M FrMacBegin B 0 FmP F FmOP 148.174 660.631 M (2,2)S FmE 1689 0 :M f148 sf ( )S 1691 0 :M FrMacBegin B 0 FmP F FmOP 158.174 664.631 M -0.12( = \(2, 3, 1\), )W FmE 1691 0 :M f203 sf ( )S 1693 0 :M FrMacBegin B 0 FmP F FmOP 207.248 664.631 M (C)S FmE 1694 0 :M f276 sf ( )S 1696 0 :M FrMacBegin B 0 FmP F FmOP 213.918 667.131 M (3)S FmE 1696 0 :M f148 sf ( )S 1698 0 :M FrMacBegin B 0 FmP F FmOP 217.918 664.631 M -0.12( )W FmE 1698 0 :M f237 sf ( )S 1700 0 :M FrMacBegin B 0 FmP F FmOP 220.298 664.631 M (\254)S FmE 1701 0 :M f148 sf ( )S 1703 0 :M FrMacBegin B 0 FmP F FmOP 230.166 664.631 M -0.12( \(0, 0, 2\) after the increment, )W FmE 1703 0 :M f203 sf ( )S 1705 0 :M FrMacBegin B 0 FmP F FmOP 346.485 664.631 M (C)S FmE 1706 0 :M f276 sf ( )S 1708 0 :M FrMacBegin B 0 FmP F FmOP 353.155 667.131 M (3)S FmE 1708 0 :M f148 sf ( )S 1710 0 :M FrMacBegin B 0 FmP F FmOP 357.155 664.631 M -0.12([0] )W FmE 1710 0 :M f237 sf ( )S 1712 0 :M FrMacBegin B 0 FmP F FmOP 371.19 664.631 M (\254)S FmE 1713 0 :M f148 sf ( )S 1715 0 :M FrMacBegin B 0 FmP F FmOP 381.058 664.631 M -0.12( max\()W FmE 1715 0 :M f203 sf ( )S 1717 0 :M FrMacBegin B 0 FmP F FmOP 403.982 664.631 M (C)S FmE 1718 0 :M f276 sf ( )S 1720 0 :M FrMacBegin B 0 FmP F FmOP 410.652 667.131 M (3)S FmE 1720 0 :M f148 sf ( )S 1722 0 :M FrMacBegin B 0 FmP F FmOP 414.652 664.631 M -0.12([0], )W FmE 1722 0 :M f203 sf ( )S 1724 0 :M FrMacBegin B 0 FmP F FmOP 431.187 664.631 M (t)S FmE 1725 0 :M f276 sf ( )S 1727 0 :M FrMacBegin B 0 FmP F FmOP 433.965 660.631 M (2,2)S FmE 1727 0 :M f148 sf ( )S 1729 0 :M FrMacBegin B 0 FmP F FmOP 443.965 664.631 M -0.12([0]\) = max\(2, 0\) = 2,)W FmE 1729 0 :M f203 sf ( )S 1731 0 :M FrMacBegin B 0 FmP F FmOP 76 681.13 M (C)S FmE 1732 0 :M f276 sf ( )S 1734 0 :M FrMacBegin B 0 FmP F FmOP 82.67 683.63 M (3)S FmE 1734 0 :M f148 sf ( )S 1736 0 :M FrMacBegin B 0 FmP F FmOP 86.67 681.13 M ([1] )S FmE 1736 0 :M f237 sf ( )S 1738 0 :M FrMacBegin B 0 FmP F FmOP 100.825 681.13 M (\254)S FmE 1739 0 :M f148 sf ( )S 1741 0 :M FrMacBegin B 0 FmP F FmOP 110.693 681.13 M ( max\()S FmE 1741 0 :M f203 sf ( )S 1743 0 :M FrMacBegin B 0 FmP F FmOP 133.738 681.13 M (C)S FmE 1744 0 :M f276 sf ( )S 1746 0 :M FrMacBegin B 0 FmP F FmOP 140.408 683.63 M (3)S FmE 1746 0 :M f148 sf ( )S 1748 0 :M FrMacBegin B 0 FmP F FmOP 144.408 681.13 M ([1], )S FmE 1748 0 :M f203 sf ( )S 1750 0 :M FrMacBegin B 0 FmP F FmOP 161.063 681.13 M (t)S FmE 1751 0 :M f276 sf ( )S 1753 0 :M FrMacBegin B 0 FmP F FmOP 163.841 677.13 M (2,2)S FmE 1753 0 :M f148 sf ( )S 1755 0 :M FrMacBegin B 0 FmP F FmOP 173.841 681.13 M ([1]\) = max\(3, 0\) = 3, and )S FmE 1755 0 :M f203 sf ( )S 1757 0 :M FrMacBegin B 0 FmP F FmOP 275.914 681.13 M (C)S FmE 1758 0 :M f276 sf ( )S 1760 0 :M FrMacBegin B 0 FmP F FmOP 282.584 683.63 M (3)S FmE 1760 0 :M f148 sf ( )S 1762 0 :M FrMacBegin B 0 FmP F FmOP 286.584 681.13 M ([2] )S FmE 1762 0 :M f237 sf ( )S 1764 0 :M FrMacBegin B 0 FmP F FmOP 300.739 681.13 M (\254)S FmE 1765 0 :M f148 sf ( )S 1767 0 :M FrMacBegin B 0 FmP F FmOP 310.607 681.13 M ( max\()S FmE 1767 0 :M f203 sf ( )S 1769 0 :M FrMacBegin B 0 FmP F FmOP 333.652 681.13 M (C)S FmE 1770 0 :M f276 sf ( )S 1772 0 :M FrMacBegin B 0 FmP F FmOP 340.322 683.63 M (3)S FmE 1772 0 :M f148 sf ( )S 1774 0 :M FrMacBegin B 0 FmP F FmOP 344.322 681.13 M ([2], )S FmE 1774 0 :M f203 sf ( )S 1776 0 :M FrMacBegin B 0 FmP F FmOP 360.977 681.13 M (t)S FmE 1777 0 :M f276 sf ( )S 1779 0 :M FrMacBegin B 0 FmP F FmOP 363.755 677.13 M (2,2)S FmE 1779 0 :M f148 sf ( )S 1781 0 :M FrMacBegin B 0 FmP F FmOP 373.755 681.13 M ([2]\) = max\(1, 2\) = 2)S 58 694.964 M (Notice that )S FmE 1781 0 :M f203 sf ( )S 1783 0 :M FrMacBegin B 0 FmP F FmOP 104.648 694.964 M (C)S FmE 1784 0 :M f276 sf ( )S 1786 0 :M FrMacBegin B 0 FmP F FmOP 111.318 697.464 M (1)S FmE 1786 0 :M f148 sf ( )S 1788 0 :M FrMacBegin B 0 FmP F FmOP 115.318 694.964 M (\()S FmE 1788 0 :M f203 sf ( )S 1790 0 :M FrMacBegin B 0 FmP F FmOP 118.646 694.964 M (e)S FmE 1791 0 :M f276 sf ( )S 1793 0 :M FrMacBegin B 0 FmP F FmOP 123.084 697.464 M (11)S FmE 1793 0 :M f148 sf ( )S 1795 0 :M FrMacBegin B 0 FmP F FmOP 131.084 694.964 M (\) < )S FmE 1795 0 :M f203 sf ( )S 1797 0 :M FrMacBegin B 0 FmP F FmOP 145.051 694.964 M (C)S FmE 1798 0 :M f276 sf ( )S 1800 0 :M FrMacBegin B 0 FmP F FmOP 151.721 697.464 M (3)S FmE 1800 0 :M f148 sf ( )S 1802 0 :M FrMacBegin B 0 FmP F FmOP 155.721 694.964 M (\()S FmE 1802 0 :M f203 sf ( )S 1804 0 :M FrMacBegin B 0 FmP F FmOP 159.049 694.964 M (e)S FmE 1805 0 :M f276 sf ( )S 1807 0 :M FrMacBegin B 0 FmP F FmOP 163.487 697.464 M (32)S FmE 1807 0 :M f148 sf ( )S 1809 0 :M FrMacBegin B 0 FmP F FmOP 171.487 694.964 M (\), so )S FmE 1809 0 :M f203 sf ( )S 1811 0 :M FrMacBegin B 0 FmP F FmOP 191.204 694.964 M (e)S FmE 1812 0 :M f276 sf ( )S 1814 0 :M FrMacBegin B 0 FmP F FmOP 195.643 697.464 M (11)S FmE 1814 0 :M f148 sf ( )S 1816 0 :M FrMacBegin B 0 FmP F FmOP 203.643 694.964 M ( )S FmE 1816 0 :M f237 sf ( )S 1818 0 :M FrMacBegin B 0 FmP F FmOP 206.143 694.964 M (\256)S FmE 1819 0 :M f148 sf ( )S 1821 0 :M FrMacBegin B 0 FmP F FmOP 216.011 694.964 M ( )S FmE 1821 0 :M f203 sf ( )S 1823 0 :M FrMacBegin B 0 FmP F FmOP 218.511 694.964 M (e)S FmE 1824 0 :M f276 sf ( )S 1826 0 :M FrMacBegin B 0 FmP F FmOP 222.949 697.464 M (32)S FmE 1826 0 :M f148 sf ( )S 1828 0 :M FrMacBegin B 0 FmP F FmOP 230.949 694.964 M (, b)S -0.2 N (ut )S FmE 1828 0 :M f203 sf ( )S 1830 0 :M FrMacBegin B 0 FmP F FmOP 251.027 694.964 M (C)S FmE 1831 0 :M f276 sf ( )S 1833 0 :M FrMacBegin B 0 FmP F FmOP 257.697 697.464 M (1)S FmE 1833 0 :M f148 sf ( )S 1835 0 :M FrMacBegin B 0 FmP F FmOP 261.697 694.964 M (\()S FmE 1835 0 :M f203 sf ( )S 1837 0 :M FrMacBegin B 0 FmP F FmOP 265.025 694.964 M (e)S FmE 1838 0 :M f276 sf ( )S 1840 0 :M FrMacBegin B 0 FmP F FmOP 269.463 697.464 M (11)S FmE 1840 0 :M f148 sf ( )S 1842 0 :M FrMacBegin B 0 FmP F FmOP 277.463 694.964 M (\) and )S FmE 1842 0 :M f203 sf ( )S 1844 0 :M FrMacBegin B 0 FmP F FmOP 300.229 694.964 M (C)S FmE 1845 0 :M f276 sf ( )S 1847 0 :M FrMacBegin B 0 FmP F FmOP 306.899 697.464 M (3)S FmE 1847 0 :M f148 sf ( )S 1849 0 :M FrMacBegin B 0 FmP F FmOP 310.899 694.964 M (\()S FmE 1849 0 :M f203 sf ( )S 1851 0 :M FrMacBegin B 0 FmP F FmOP 314.227 694.964 M (e)S FmE 1852 0 :M f276 sf ( )S 1854 0 :M FrMacBegin B 0 FmP F FmOP 318.666 697.464 M (31)S FmE 1854 0 :M f148 sf ( )S 1856 0 :M FrMacBegin B 0 FmP F FmOP 326.666 694.964 M (\) are incomparable, so )S FmE 1856 0 :M f203 sf ( )S 1858 0 :M FrMacBegin B 0 FmP F FmOP 418.003 694.964 M (e)S FmE 1859 0 :M f276 sf ( )S 1861 0 :M FrMacBegin B 0 FmP F FmOP 422.442 697.464 M (11)S FmE 1861 0 :M f148 sf ( )S 1863 0 :M FrMacBegin B 0 FmP F FmOP 430.442 694.964 M ( and )S FmE 1863 0 :M f203 sf ( )S 1865 0 :M FrMacBegin B 0 FmP F FmOP 449.88 694.964 M (e)S FmE 1866 0 :M f276 sf ( )S 1868 0 :M FrMacBegin B 0 FmP F FmOP 454.319 697.464 M (31)S FmE 1868 0 :M f148 sf ( )S 1870 0 :M FrMacBegin B 0 FmP F FmOP 462.319 694.964 M ( are concurrent.)S FmE 58 337 468 121 rC 1870 0 :M FrMacBegin 58 337.466 468 120 FmKp B 0 FmP F FmOP 110 359.036 FmB 378 0 FmL 2 1 FmSo 110 395.036 FmB 378 0 FmL 2 1 FmSo 110 440.036 FmB 378 0 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 141.5 358.536 FmAF T 0 360 4.5 4.5 0 141.5 358.536 2 1 F FmAP 0 360 4.5 4.5 0 T 257.5 359.203 FmAF T 0 360 4.5 4.5 0 257.5 359.203 2 1 F FmAP 0 360 4.5 4.5 0 T 198.833 395.203 FmAF T 0 360 4.5 4.5 0 198.833 395.203 2 1 F FmAP 0 360 4.5 4.5 0 T 249.5 395.203 FmAF T 0 360 4.5 4.5 0 249.5 395.203 2 1 F FmAP 0 360 4.5 4.5 0 T 161.5 441.203 FmAF T 0 360 4.5 4.5 0 161.5 441.203 2 1 F FmAP 0 360 4.5 4.5 0 T 363.5 395.203 FmAF T 0 360 4.5 4.5 0 363.5 395.203 2 1 F FmAP 0 360 4.5 4.5 0 T 437.5 440.536 FmAF T 0 360 4.5 4.5 0 437.5 440.536 2 1 F FmAP 0 360 4.5 4.5 0 T 434.833 359.87 FmAF T 0 360 4.5 4.5 0 434.833 359.87 2 1 F FmAP FmE 1870 0 :M f289 sf ( )S 1873 0 :M FrMacBegin 58 337.466 468 120 FmKp B 0 FmP F FmOP 89.333 359.403 M (P)S FmE 1873 0 :M f148 sf ( )S 1875 0 :M FrMacBegin 58 337.466 468 120 FmKp B 0 FmP F FmOP FmG 96.663 362.403 M 0.96 0.96 scale (1)S FmR FmE 1876 0 :M f289 sf ( )S 1879 0 :M FrMacBegin 58 337.466 468 120 FmKp B 0 FmP F FmOP 89.333 396.737 M (P)S FmE 1879 0 :M f148 sf ( )S 1881 0 :M FrMacBegin 58 337.466 468 120 FmKp B 0 FmP F FmOP FmG 96.663 399.737 M 0.96 0.96 scale (2)S FmR FmE 1881 0 :M f289 sf ( )S 1884 0 :M FrMacBegin 58 337.466 468 120 FmKp B 0 FmP F FmOP 89.333 443.403 M (P)S FmE 1884 0 :M f148 sf ( )S 1886 0 :M FrMacBegin 58 337.466 468 120 FmKp B 0 FmP F FmOP FmG 96.663 446.403 M 0.96 0.96 scale (3)S FmR FmG 138 351.07 M 0.96 0.96 scale (e11)S FmR FmG 257.333 353.07 M 0.96 0.96 scale (e12)S FmR FmG 196.667 387.737 M 0.96 0.96 scale (e21)S FmR FmG 250 387.737 M 0.96 0.96 scale (e22)S FmR FmG 340 387.737 M 0.96 0.96 scale (e23)S FmR FmG 145.333 432.403 M 0.96 0.96 scale (e31)S FmR FmG 436 433.07 M 0.96 0.96 scale (e32)S FmR FmG 428.667 352.403 M 0.96 0.96 scale (e13)S FmR 325.693 386.364 FmB 1.257 -3.235 FmL 10.027 7.618 FmL -12.54 -1.147 FmL 1 FmS 325.693 386.364 FmB 1.257 -3.235 FmL 10.027 7.618 FmL -12.54 -1.147 FmL FmFl 258 360.07 FmB 67.227 26.113 FmL 2 1 FmSo 416.972 363.208 FmB -0.616 -3.416 FmL 12.529 1.266 FmL -11.296 5.565 FmL 1 FmS 416.972 363.208 FmB -0.616 -3.416 FmL 12.529 1.266 FmL -11.296 5.565 FmL FmFl 253.333 392.737 FmB 163.146 -29.44 FmL 2 1 FmSo 421.241 429.844 FmB 1.719 -3.015 FmL 8.798 9.01 FmL -12.235 -2.979 FmL 1 FmS 421.241 429.844 FmB 1.719 -3.015 FmL 8.798 9.01 FmL -12.235 -2.979 FmL FmFl 366.667 398.737 FmB 54.14 30.86 FmL 2 1 FmSo 188.319 408.675 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL 1 FmS 188.319 408.675 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL FmFl 163.333 438.07 FmB 24.662 -29.014 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 340.167 395.203 FmAF T 0 360 4.5 4.5 0 340.167 395.203 2 1 F FmAP 371.333 385.403 M (e24)S FmE endp showpage %%PageTrailer %%Page: 4 4 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 4 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 1887 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 1887 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 1887 0 :M f148 sf ( )S 1889 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Birman-Schiper-Stephenson Protocol)S 36.275 N (ECS 251 \320 Winter 2001)S 159.015 N (Page )S (4)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 1890 0 :M f175 sf ( )S 1894 0 :M FrMacBegin B 0 FmP F FmOP 148.751 72 M (Birman-Schiper)S -0.668 N (-Stephenson Pr)S -0.325 N (otocol)S FmE 1894 0 :M f263 sf ( )S 1897 0 :M FrMacBegin B 0 FmP F FmOP 58 104 M (Intr)S -0.217 N (oduction)S FmE 1897 0 :M f148 sf ( )S 1899 0 :M FrMacBegin B 0 FmP F FmOP 58 121.667 M (The goal of this protocol is to preserv)S -0.151 N (e ordering in the sending of messages. F)S -0.151 N (or e)S -0.151 N (xample, if )S FmE 1900 0 :M f203 sf ( )S 1902 0 :M FrMacBegin B 0 FmP F FmOP 427.138 121.667 M (send)S FmE 1902 0 :M f148 sf ( )S 1904 0 :M FrMacBegin B 0 FmP F FmOP 445.466 121.667 M (\()S FmE 1905 0 :M f203 sf ( )S 1907 0 :M FrMacBegin B 0 FmP F FmOP 448.793 121.667 M (m)S FmE 1907 0 :M f276 sf ( )S 1909 0 :M FrMacBegin B 0 FmP F FmOP 456.013 124.167 M (1)S FmE 1909 0 :M f148 sf ( )S 1911 0 :M FrMacBegin B 0 FmP F FmOP 460.013 121.667 M (\) )S FmE 1912 0 :M f237 sf ( )S 1914 0 :M FrMacBegin B 0 FmP F FmOP 465.84 121.667 M (\256)S FmE 1914 0 :M f148 sf ( )S 1916 0 :M FrMacBegin B 0 FmP F FmOP 475.708 121.667 M ( send\()S FmE 1917 0 :M f203 sf ( )S 1919 0 :M FrMacBegin B 0 FmP F FmOP 499.864 121.667 M (m)S FmE 1919 0 :M f276 sf ( )S 1921 0 :M FrMacBegin B 0 FmP F FmOP 507.083 124.167 M (2)S FmE 1921 0 :M f148 sf ( )S 1923 0 :M FrMacBegin B 0 FmP F FmOP 511.083 121.667 M (\), )S 58 135.5 M -0.198(then for all processes that recei)W -0.251 N (v)S -0.151 N -0.198(e both )W FmE 1924 0 :M f203 sf ( )S 1926 0 :M FrMacBegin B 0 FmP F FmOP 212.519 135.5 M (m)S FmE 1926 0 :M f276 sf ( )S 1928 0 :M FrMacBegin B 0 FmP F FmOP 219.738 138 M (1)S FmE 1928 0 :M f148 sf ( )S 1930 0 :M FrMacBegin B 0 FmP F FmOP 223.738 135.5 M -0.198( and )W FmE 1931 0 :M f203 sf ( )S 1933 0 :M FrMacBegin B 0 FmP F FmOP 242.78 135.5 M (m)S FmE 1933 0 :M f276 sf ( )S 1935 0 :M FrMacBegin B 0 FmP F FmOP 249.999 138 M (2)S FmE 1935 0 :M f148 sf ( )S 1937 0 :M FrMacBegin B 0 FmP F FmOP 253.999 135.5 M -0.198(, )W FmE 1938 0 :M f203 sf ( )S 1940 0 :M FrMacBegin B 0 FmP F FmOP 258.8 135.5 M (r)S -0.371 N (eceive)S FmE 1940 0 :M f148 sf ( )S 1942 0 :M FrMacBegin B 0 FmP F FmOP 287.289 135.5 M (\()S FmE 1943 0 :M f203 sf ( )S 1945 0 :M FrMacBegin B 0 FmP F FmOP 290.617 135.5 M (m)S FmE 1945 0 :M f276 sf ( )S 1947 0 :M FrMacBegin B 0 FmP F FmOP 297.836 138 M (1)S FmE 1947 0 :M f148 sf ( )S 1949 0 :M FrMacBegin B 0 FmP F FmOP 301.836 135.5 M (\))S FmE 1950 0 :M f237 sf ( )S 1952 0 :M FrMacBegin B 0 FmP F FmOP 305.164 135.5 M (\256)S FmE 1952 0 :M f148 sf ( )S 1954 0 :M FrMacBegin B 0 FmP F FmOP 315.032 135.5 M -0.198( )W FmE 1955 0 :M f203 sf ( )S 1957 0 :M FrMacBegin B 0 FmP F FmOP 317.333 135.5 M (r)S -0.371 N (eceive)S FmE 1957 0 :M f148 sf ( )S 1959 0 :M FrMacBegin B 0 FmP F FmOP 345.822 135.5 M (\()S FmE 1960 0 :M f203 sf ( )S 1962 0 :M FrMacBegin B 0 FmP F FmOP 349.15 135.5 M (m)S FmE 1962 0 :M f276 sf ( )S 1964 0 :M FrMacBegin B 0 FmP F FmOP 356.369 138 M (2)S FmE 1964 0 :M f148 sf ( )S 1966 0 :M FrMacBegin B 0 FmP F FmOP 360.369 135.5 M -0.198(\). )W -0.181 N -0.198(The basic idea is that )W FmE 1967 0 :M f203 sf ( )S 1969 0 :M FrMacBegin B 0 FmP F FmOP 454.234 135.5 M (m)S FmE 1969 0 :M f276 sf ( )S 1971 0 :M FrMacBegin B 0 FmP F FmOP 461.453 138 M (2)S FmE 1971 0 :M f148 sf ( )S 1973 0 :M FrMacBegin B 0 FmP F FmOP 465.453 135.5 M -0.198( is not gi)W -0.251 N (v)S -0.151 N -0.198(en to )W 58 149.333 M (the process until )S FmE 1974 0 :M f203 sf ( )S 1976 0 :M FrMacBegin B 0 FmP F FmOP 126.035 149.333 M (m)S FmE 1976 0 :M f276 sf ( )S 1978 0 :M FrMacBegin B 0 FmP F FmOP 133.254 151.833 M (1)S FmE 1978 0 :M f148 sf ( )S 1980 0 :M FrMacBegin B 0 FmP F FmOP 137.254 149.333 M ( is gi)S -0.251 N (v)S -0.151 N (en. )S -0.181 N (This means a b)S -0.2 N (uf)S -0.251 N (fer is needed for pending deli)S -0.251 N (v)S -0.151 N (eries. )S -0.552 N (Also, each message has an associ-)S 58 163.167 M (ated v)S -0.151 N (ector that contains information for the recipient to determine if another message preceded it. )S -0.552 N (Also, we shall )S 58 175.166 M (assume all messages are broadcast. Clocks are updated only when messages are sent.)S FmE 1981 0 :M f263 sf ( )S 1984 0 :M FrMacBegin B 0 FmP F FmOP 58 200.5 M (Notation)S FmE 1984 0 :M f148 sf ( )S 1986 0 :M FrMacBegin B 0 FmP F FmOP 58 218.166 M (\245)S FmE 1986 0 :M f203 sf ( )S 1988 0 :M FrMacBegin B 0 FmP F FmOP 76 218.166 M (n)S FmE 1989 0 :M f148 sf ( )S 1991 0 :M FrMacBegin B 0 FmP F FmOP 81 218.166 M ( processes)S 58 230.166 M (\245)S FmE 1991 0 :M f203 sf ( )S 1993 0 :M FrMacBegin B 0 FmP F FmOP 76 230.166 M (P)S FmE 1994 0 :M f250 sf ( )S 1996 0 :M FrMacBegin B 0 FmP F FmOP 82.108 232.666 M (i)S FmE 1996 0 :M f148 sf ( )S 1998 0 :M FrMacBegin B 0 FmP F FmOP 84.331 230.166 M ( process)S 58 244 M (\245)S FmE 1998 0 :M f203 sf ( )S 2000 0 :M FrMacBegin B 0 FmP F FmOP 76 244 M (C)S FmE 2001 0 :M f250 sf ( )S 2003 0 :M FrMacBegin B 0 FmP F FmOP 82.67 246.5 M (i)S FmE 2003 0 :M f148 sf ( )S 2005 0 :M FrMacBegin B 0 FmP F FmOP 84.893 244 M -0.013(. v)W -0.151 N -0.013(ector clock associated with process )W FmE 2005 0 :M f203 sf ( )S 2007 0 :M FrMacBegin B 0 FmP F FmOP 237.65 244 M (P)S FmE 2008 0 :M f250 sf ( )S 2010 0 :M FrMacBegin B 0 FmP F FmOP 243.759 246.5 M (i)S FmE 2010 0 :M f148 sf ( )S 2012 0 :M FrMacBegin B 0 FmP F FmOP 245.981 244 M -0.013(; )W FmE 2012 0 :M f203 sf ( )S 2014 0 :M FrMacBegin B 0 FmP F FmOP 251.247 244 M (j)S FmE 2015 0 :M f148 sf ( )S 2017 0 :M FrMacBegin B 0 FmP F FmOP 254.025 244 M -0.013(th element is )W FmE 2017 0 :M f203 sf ( )S 2019 0 :M FrMacBegin B 0 FmP F FmOP 307.583 244 M (C)S FmE 2020 0 :M f250 sf ( )S 2022 0 :M FrMacBegin B 0 FmP F FmOP 314.253 246.5 M (i)S FmE 2022 0 :M f148 sf ( )S 2024 0 :M FrMacBegin B 0 FmP F FmOP 316.476 244 M ([)S FmE 2024 0 :M f203 sf ( )S 2026 0 :M FrMacBegin B 0 FmP F FmOP 319.803 244 M (j)S FmE 2027 0 :M f148 sf ( )S 2029 0 :M FrMacBegin B 0 FmP F FmOP 322.582 244 M -0.013(] and contains )W FmE 2029 0 :M f203 sf ( )S 2031 0 :M FrMacBegin B 0 FmP F FmOP 381.132 244 M (P)S FmE 2032 0 :M f250 sf ( )S 2034 0 :M FrMacBegin B 0 FmP F FmOP 387.241 246.5 M (i)S FmE 2034 0 :M f148 sf ( )S 2036 0 :M FrMacBegin B 0 FmP F FmOP 389.463 244 M (\325)S -0.552 N -0.013(s latest v)W -0.251 N -0.013(alue for the current time )W 76 257.833 M (in process )S FmE 2036 0 :M f203 sf ( )S 2038 0 :M FrMacBegin B 0 FmP F FmOP 118.761 257.833 M (P)S FmE 2039 0 :M f250 sf ( )S 2041 0 :M FrMacBegin B 0 FmP F FmOP 124.87 260.333 M (k)S FmE 2041 0 :M f148 sf ( )S 2043 0 :M FrMacBegin B 0 FmP F FmOP 128.42 257.833 M (.)S 58 274.333 M (\245)S FmE 2043 0 :M f203 sf ( )S 2045 0 :M FrMacBegin B 0 FmP F FmOP 76 274.333 M (t)S FmE 2046 0 :M f250 sf ( )S 2048 0 :M FrMacBegin B 0 FmP F FmOP 78.778 270.333 M (m)S FmE 2048 0 :M f148 sf ( )S 2050 0 :M FrMacBegin B 0 FmP F FmOP 84.556 274.333 M ( v)S -0.151 N (ector timestamp for message )S FmE 2050 0 :M f203 sf ( )S 2052 0 :M FrMacBegin B 0 FmP F FmOP 209.072 274.333 M (m)S FmE 2053 0 :M f148 sf ( )S 2055 0 :M FrMacBegin B 0 FmP F FmOP 216.292 274.333 M ( \(stamped )S FmE 2055 0 :M f203 sf ( )S 2057 0 :M FrMacBegin B 0 FmP F FmOP 257.942 274.333 M (after)S FmE 2058 0 :M f148 sf ( )S 2060 0 :M FrMacBegin B 0 FmP F FmOP 276.826 274.333 M ( local clock is incremented\))S FmE 2060 0 :M f263 sf ( )S 2063 0 :M FrMacBegin B 0 FmP F FmOP 58 299.666 M (Pr)S -0.217 N (otocol)S FmE 2063 0 :M f319 sf ( )S 2065 0 :M FrMacBegin B 0 FmP F FmOP 58 317.333 M (P)S FmE 2066 0 :M f332 sf ( )S 2068 0 :M FrMacBegin B 0 FmP F FmOP 64.108 319.833 M (i)S FmE 2068 0 :M f345 sf ( )S 2070 0 :M FrMacBegin B 0 FmP F FmOP 66.331 317.333 M ( br)S -0.181 N (oadcasts a message)S FmE 2070 0 :M f148 sf ( )S 2072 0 :M FrMacBegin B 0 FmP F FmOP 58 333.833 M (1.)S FmE 2073 0 :M f203 sf ( )S 2075 0 :M FrMacBegin B 0 FmP F FmOP 76 333.833 M (P)S FmE 2075 0 :M f250 sf ( )S 2077 0 :M FrMacBegin B 0 FmP F FmOP 82.108 336.333 M (i)S FmE 2077 0 :M f148 sf ( )S 2079 0 :M FrMacBegin B 0 FmP F FmOP 84.331 333.833 M ( increments )S FmE 2080 0 :M f203 sf ( )S 2082 0 :M FrMacBegin B 0 FmP F FmOP 133.198 333.833 M (C)S FmE 2082 0 :M f250 sf ( )S 2084 0 :M FrMacBegin B 0 FmP F FmOP 139.868 336.333 M (i)S FmE 2084 0 :M f148 sf ( )S 2086 0 :M FrMacBegin B 0 FmP F FmOP 142.091 333.833 M ([)S FmE 2087 0 :M f203 sf ( )S 2089 0 :M FrMacBegin B 0 FmP F FmOP 145.418 333.833 M (i)S FmE 2089 0 :M f148 sf ( )S 2091 0 :M FrMacBegin B 0 FmP F FmOP 148.197 333.833 M (] and sets the timestamp )S FmE 2092 0 :M f203 sf ( )S 2094 0 :M FrMacBegin B 0 FmP F FmOP 247.333 333.833 M (t)S FmE 2094 0 :M f250 sf ( )S 2096 0 :M FrMacBegin B 0 FmP F FmOP 250.111 329.833 M (m)S FmE 2096 0 :M f148 sf ( )S 2098 0 :M FrMacBegin B 0 FmP F FmOP 255.888 333.833 M ( = )S FmE 2099 0 :M f203 sf ( )S 2101 0 :M FrMacBegin B 0 FmP F FmOP 269.028 333.833 M (C)S FmE 2101 0 :M f250 sf ( )S 2103 0 :M FrMacBegin B 0 FmP F FmOP 275.698 336.333 M (i)S FmE 2103 0 :M f148 sf ( )S 2105 0 :M FrMacBegin B 0 FmP F FmOP 277.92 333.833 M ( for message )S FmE 2106 0 :M f203 sf ( )S 2108 0 :M FrMacBegin B 0 FmP F FmOP 330.948 333.833 M (m)S FmE 2108 0 :M f148 sf ( )S 2110 0 :M FrMacBegin B 0 FmP F FmOP 338.167 333.833 M (. )S FmE 2111 0 :M f319 sf ( )S 2113 0 :M FrMacBegin B 0 FmP F FmOP 58 347.666 M (P)S FmE 2113 0 :M f332 sf ( )S 2115 0 :M FrMacBegin B 0 FmP F FmOP 64.108 350.166 M (j)S FmE 2115 0 :M f345 sf ( )S 2117 0 :M FrMacBegin B 0 FmP F FmOP 66.331 347.666 M ( r)S -0.181 N (ecei)S -0.1 N (v)S -0.1 N (es a message fr)S -0.181 N (om )S FmE 2118 0 :M f319 sf ( )S 2120 0 :M FrMacBegin B 0 FmP F FmOP 173.206 347.666 M (P)S FmE 2120 0 :M f332 sf ( )S 2122 0 :M FrMacBegin B 0 FmP F FmOP 179.314 350.166 M (i)S FmE 2122 0 :M f148 sf ( )S 2124 0 :M FrMacBegin B 0 FmP F FmOP 58 364.166 M (1.)S 10.5 N (When )S FmE 2125 0 :M f203 sf ( )S 2127 0 :M FrMacBegin B 0 FmP F FmOP 102.377 364.166 M (P)S FmE 2127 0 :M f250 sf ( )S 2129 0 :M FrMacBegin B 0 FmP F FmOP 108.485 366.666 M (j)S FmE 2129 0 :M f148 sf ( )S 2131 0 :M FrMacBegin B 0 FmP F FmOP 110.708 364.166 M (, )S FmE 2132 0 :M f203 sf ( )S 2134 0 :M FrMacBegin B 0 FmP F FmOP 115.708 364.166 M (j)S FmE 2134 0 :M f148 sf ( )S 2136 0 :M FrMacBegin B 0 FmP F FmOP 118.486 364.166 M ( )S FmE 2137 0 :M f237 sf ( )S 2139 0 :M FrMacBegin B 0 FmP F FmOP 120.986 364.166 M (\271)S FmE 2139 0 :M f148 sf ( )S 2141 0 :M FrMacBegin B 0 FmP F FmOP 126.475 364.166 M ( )S FmE 2142 0 :M f203 sf ( )S 2144 0 :M FrMacBegin B 0 FmP F FmOP 128.975 364.166 M (i)S FmE 2144 0 :M f148 sf ( )S 2146 0 :M FrMacBegin B 0 FmP F FmOP 131.753 364.166 M (, recei)S -0.251 N (v)S -0.151 N (es )S FmE 2147 0 :M f203 sf ( )S 2149 0 :M FrMacBegin B 0 FmP F FmOP 171.599 364.166 M (m)S FmE 2149 0 :M f148 sf ( )S 2151 0 :M FrMacBegin B 0 FmP F FmOP 178.818 364.166 M ( with timestamp )S FmE 2152 0 :M f203 sf ( )S 2154 0 :M FrMacBegin B 0 FmP F FmOP 245.752 364.166 M (t)S FmE 2154 0 :M f250 sf ( )S 2156 0 :M FrMacBegin B 0 FmP F FmOP 248.53 360.166 M (m)S FmE 2156 0 :M f148 sf ( )S 2158 0 :M FrMacBegin B 0 FmP F FmOP 254.308 364.166 M (, it delays the message\325)S -0.552 N (s deli)S -0.251 N (v)S -0.151 N (ery until )S FmE 2159 0 :M f203 sf ( )S 2161 0 :M FrMacBegin B 0 FmP F FmOP 408.856 364.166 M (both)S FmE 2161 0 :M f148 sf ( )S 2163 0 :M FrMacBegin B 0 FmP F FmOP 426.634 364.166 M (:)S 76 380.666 M (a.)S FmE 2164 0 :M f203 sf ( )S 2166 0 :M FrMacBegin B 0 FmP F FmOP 94 380.666 M (C)S FmE 2166 0 :M f250 sf ( )S 2168 0 :M FrMacBegin B 0 FmP F FmOP 100.67 383.166 M (j)S FmE 2168 0 :M f148 sf ( )S 2170 0 :M FrMacBegin B 0 FmP F FmOP 102.893 380.666 M ([)S FmE 2171 0 :M f203 sf ( )S 2173 0 :M FrMacBegin B 0 FmP F FmOP 106.22 380.666 M (i)S FmE 2173 0 :M f148 sf ( )S 2175 0 :M FrMacBegin B 0 FmP F FmOP 108.999 380.666 M (] = )S FmE 2176 0 :M f203 sf ( )S 2178 0 :M FrMacBegin B 0 FmP F FmOP 122.966 380.666 M (t)S FmE 2178 0 :M f250 sf ( )S 2180 0 :M FrMacBegin B 0 FmP F FmOP 125.744 376.666 M (m)S FmE 2180 0 :M f148 sf ( )S 2182 0 :M FrMacBegin B 0 FmP F FmOP 131.521 380.666 M ([)S FmE 2183 0 :M f203 sf ( )S 2185 0 :M FrMacBegin B 0 FmP F FmOP 134.849 380.666 M (i)S FmE 2185 0 :M f148 sf ( )S 2187 0 :M FrMacBegin B 0 FmP F FmOP 137.627 380.666 M (] \320 1; and)S 76 397.165 M (b)S -0.4 N (.)S 10.9 N (for all )S FmE 2188 0 :M f203 sf ( )S 2190 0 :M FrMacBegin B 0 FmP F FmOP 120.65 397.165 M (k)S FmE 2190 0 :M f148 sf ( )S 2192 0 :M FrMacBegin B 0 FmP F FmOP 125.089 397.165 M ( )S FmE 2193 0 :M f237 sf ( )S 2195 0 :M FrMacBegin B 0 FmP F FmOP 127.589 397.165 M (\243)S FmE 2195 0 :M f148 sf ( )S 2197 0 :M FrMacBegin B 0 FmP F FmOP 133.077 397.165 M ( )S FmE 2198 0 :M f203 sf ( )S 2200 0 :M FrMacBegin B 0 FmP F FmOP 135.577 397.165 M (n)S FmE 2200 0 :M f148 sf ( )S 2202 0 :M FrMacBegin B 0 FmP F FmOP 140.577 397.165 M ( and )S FmE 2203 0 :M f203 sf ( )S 2205 0 :M FrMacBegin B 0 FmP F FmOP 160.016 397.165 M (k)S FmE 2205 0 :M f148 sf ( )S 2207 0 :M FrMacBegin B 0 FmP F FmOP 164.454 397.165 M ( )S FmE 2208 0 :M f237 sf ( )S 2210 0 :M FrMacBegin B 0 FmP F FmOP 166.954 397.165 M (\271)S FmE 2210 0 :M f148 sf ( )S 2212 0 :M FrMacBegin B 0 FmP F FmOP 172.442 397.165 M ( )S FmE 2213 0 :M f203 sf ( )S 2215 0 :M FrMacBegin B 0 FmP F FmOP 174.942 397.165 M (i)S FmE 2215 0 :M f148 sf ( )S 2217 0 :M FrMacBegin B 0 FmP F FmOP 177.721 397.165 M (, )S FmE 2218 0 :M f203 sf ( )S 2220 0 :M FrMacBegin B 0 FmP F FmOP 182.721 397.165 M (C)S FmE 2220 0 :M f250 sf ( )S 2222 0 :M FrMacBegin B 0 FmP F FmOP 189.391 399.665 M (j)S FmE 2222 0 :M f148 sf ( )S 2224 0 :M FrMacBegin B 0 FmP F FmOP 191.613 397.165 M ([)S FmE 2225 0 :M f203 sf ( )S 2227 0 :M FrMacBegin B 0 FmP F FmOP 194.941 397.165 M (k)S FmE 2227 0 :M f148 sf ( )S 2229 0 :M FrMacBegin B 0 FmP F FmOP 199.379 397.165 M (] )S FmE 2230 0 :M f237 sf ( )S 2232 0 :M FrMacBegin B 0 FmP F FmOP 205.207 397.165 M (\263)S FmE 2232 0 :M f148 sf ( )S 2234 0 :M FrMacBegin B 0 FmP F FmOP 210.695 397.165 M ( )S FmE 2235 0 :M f203 sf ( )S 2237 0 :M FrMacBegin B 0 FmP F FmOP 215.695 397.165 M (t)S FmE 2237 0 :M f250 sf ( )S 2239 0 :M FrMacBegin B 0 FmP F FmOP 218.474 393.165 M (m)S FmE 2239 0 :M f148 sf ( )S 2241 0 :M FrMacBegin B 0 FmP F FmOP 224.251 397.165 M ([)S FmE 2242 0 :M f203 sf ( )S 2244 0 :M FrMacBegin B 0 FmP F FmOP 227.579 397.165 M (k)S FmE 2244 0 :M f148 sf ( )S 2246 0 :M FrMacBegin B 0 FmP F FmOP 232.017 397.165 M (].)S 58 413.965 M (2.)S 10.5 N (When the message is deli)S -0.251 N (v)S -0.151 N (ered to )S FmE 2247 0 :M f203 sf ( )S 2249 0 :M FrMacBegin B 0 FmP F FmOP 212.208 413.965 M (P)S FmE 2249 0 :M f250 sf ( )S 2251 0 :M FrMacBegin B 0 FmP F FmOP 218.317 416.465 M (j)S FmE 2251 0 :M f148 sf ( )S 2253 0 :M FrMacBegin B 0 FmP F FmOP 220.54 413.965 M (, update )S FmE 2254 0 :M f203 sf ( )S 2256 0 :M FrMacBegin B 0 FmP F FmOP 254.695 413.965 M (P)S FmE 2256 0 :M f250 sf ( )S 2258 0 :M FrMacBegin B 0 FmP F FmOP 260.803 416.465 M (j)S FmE 2258 0 :M f148 sf ( )S 2260 0 :M FrMacBegin B 0 FmP F FmOP 263.026 413.965 M (\325)S -0.552 N (s v)S -0.151 N (ector clock for all )S FmE 2261 0 :M f203 sf ( )S 2263 0 :M FrMacBegin B 0 FmP F FmOP 350.328 413.965 M (k)S FmE 2263 0 :M f148 sf ( )S 2265 0 :M FrMacBegin B 0 FmP F FmOP 354.767 413.965 M ( = 1, \311, )S FmE 2266 0 :M f203 sf ( )S 2268 0 :M FrMacBegin B 0 FmP F FmOP 390.406 413.965 M (n)S FmE 2268 0 :M f148 sf ( )S 2270 0 :M FrMacBegin B 0 FmP F FmOP 395.406 413.965 M (: )S FmE 2271 0 :M f203 sf ( )S 2273 0 :M FrMacBegin B 0 FmP F FmOP 400.685 413.965 M (C)S FmE 2273 0 :M f250 sf ( )S 2275 0 :M FrMacBegin B 0 FmP F FmOP 407.354 416.465 M (j)S FmE 2275 0 :M f148 sf ( )S 2277 0 :M FrMacBegin B 0 FmP F FmOP 409.577 413.965 M ([)S FmE 2278 0 :M f203 sf ( )S 2280 0 :M FrMacBegin B 0 FmP F FmOP 412.905 413.965 M (k)S FmE 2280 0 :M f148 sf ( )S 2282 0 :M FrMacBegin B 0 FmP F FmOP 417.343 413.965 M (] )S FmE 2283 0 :M f237 sf ( )S 2285 0 :M FrMacBegin B 0 FmP F FmOP 423.171 413.965 M (\254)S FmE 2285 0 :M f148 sf ( )S 2287 0 :M FrMacBegin B 0 FmP F FmOP 433.039 413.965 M ( max\()S FmE 2288 0 :M f203 sf ( )S 2290 0 :M FrMacBegin B 0 FmP F FmOP 456.083 413.965 M (C)S FmE 2290 0 :M f250 sf ( )S 2292 0 :M FrMacBegin B 0 FmP F FmOP 462.753 416.465 M (j)S FmE 2292 0 :M f148 sf ( )S 2294 0 :M FrMacBegin B 0 FmP F FmOP 464.976 413.965 M ([)S FmE 2295 0 :M f203 sf ( )S 2297 0 :M FrMacBegin B 0 FmP F FmOP 468.304 413.965 M (k)S FmE 2297 0 :M f148 sf ( )S 2299 0 :M FrMacBegin B 0 FmP F FmOP 472.742 413.965 M (], )S FmE 2300 0 :M f203 sf ( )S 2302 0 :M FrMacBegin B 0 FmP F FmOP 481.07 413.965 M (t)S FmE 2302 0 :M f250 sf ( )S 2304 0 :M FrMacBegin B 0 FmP F FmOP 483.848 409.965 M (a)S FmE 2304 0 :M f148 sf ( )S 2306 0 :M FrMacBegin B 0 FmP F FmOP 487.848 413.965 M ([)S FmE 2307 0 :M f203 sf ( )S 2309 0 :M FrMacBegin B 0 FmP F FmOP 491.176 413.965 M (k)S FmE 2309 0 :M f148 sf ( )S 2311 0 :M FrMacBegin B 0 FmP F FmOP 495.614 413.965 M (]\))S 58 428.098 M (3.)S 10.5 N (Check b)S -0.2 N (uf)S -0.251 N (fered messages to see if an)S -0.151 N (y can be deli)S -0.251 N (v)S -0.151 N (ered.)S FmE endp showpage %%PageTrailer %%Page: 5 5 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 5 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 2312 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 2312 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 2312 0 :M f148 sf ( )S 2314 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Birman-Schiper-Stephenson Protocol)S 36.275 N (ECS 251 \320 Winter 2001)S 159.015 N (Page )S (5)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 2315 0 :M f263 sf ( )S 2318 0 :M FrMacBegin B 0 FmP F FmOP 58 68 M (Example)S FmE 2318 0 :M f148 sf ( )S 2320 0 :M FrMacBegin B 0 FmP F FmOP 58 203 M (Here is the protocol applied to the abo)S -0.151 N (v)S -0.151 N (e situation:)S FmE 2320 0 :M f203 sf ( )S 2322 0 :M FrMacBegin B 0 FmP F FmOP 58 217.666 M (e)S FmE 2323 0 :M f276 sf ( )S 2325 0 :M FrMacBegin B 0 FmP F FmOP 62.438 220.166 M (31)S FmE 2325 0 :M f148 sf ( )S 2327 0 :M FrMacBegin B 0 FmP F FmOP 70.438 217.666 M (: )S FmE 2327 0 :M f203 sf ( )S 2329 0 :M FrMacBegin B 0 FmP F FmOP 75.717 217.666 M (P)S FmE 2330 0 :M f276 sf ( )S 2332 0 :M FrMacBegin B 0 FmP F FmOP 81.825 220.166 M (3)S FmE 2332 0 :M f148 sf ( )S 2334 0 :M FrMacBegin B 0 FmP F FmOP 85.825 217.666 M ( sends message )S FmE 2334 0 :M f203 sf ( )S 2336 0 :M FrMacBegin B 0 FmP F FmOP 149.414 217.666 M (a)S FmE 2337 0 :M f148 sf ( )S 2339 0 :M FrMacBegin B 0 FmP F FmOP 154.414 217.666 M (; )S FmE 2339 0 :M f203 sf ( )S 2341 0 :M FrMacBegin B 0 FmP F FmOP 159.692 217.666 M (C)S FmE 2342 0 :M f276 sf ( )S 2344 0 :M FrMacBegin B 0 FmP F FmOP 166.362 220.166 M (3)S FmE 2344 0 :M f148 sf ( )S 2346 0 :M FrMacBegin B 0 FmP F FmOP 170.362 217.666 M ( = \(0, 0, 1\); )S FmE 2346 0 :M f203 sf ( )S 2348 0 :M FrMacBegin B 0 FmP F FmOP 217.936 217.666 M (t)S FmE 2349 0 :M f250 sf ( )S 2351 0 :M FrMacBegin B 0 FmP F FmOP 220.714 213.667 M (a)S FmE 2351 0 :M f148 sf ( )S 2353 0 :M FrMacBegin B 0 FmP F FmOP 224.714 217.666 M ( = \(0, 0, 1\))S FmE 2353 0 :M f203 sf ( )S 2355 0 :M FrMacBegin B 0 FmP F FmOP 58 234.166 M (e)S FmE 2356 0 :M f276 sf ( )S 2358 0 :M FrMacBegin B 0 FmP F FmOP 62.438 236.666 M (21)S FmE 2358 0 :M f148 sf ( )S 2360 0 :M FrMacBegin B 0 FmP F FmOP 70.438 234.166 M -0.07(: )W FmE 2360 0 :M f203 sf ( )S 2362 0 :M FrMacBegin B 0 FmP F FmOP 75.647 234.166 M (P)S FmE 2363 0 :M f276 sf ( )S 2365 0 :M FrMacBegin B 0 FmP F FmOP 81.755 236.666 M (2)S FmE 2365 0 :M f148 sf ( )S 2367 0 :M FrMacBegin B 0 FmP F FmOP 85.755 234.166 M -0.07( recei)W -0.251 N (v)S -0.151 N -0.07(es message )W FmE 2367 0 :M f203 sf ( )S 2369 0 :M FrMacBegin B 0 FmP F FmOP 159.263 234.166 M (a)S FmE 2370 0 :M f148 sf ( )S 2372 0 :M FrMacBegin B 0 FmP F FmOP 164.263 234.166 M -0.07(. )W -0.552 N -0.07(As )W FmE 2372 0 :M f203 sf ( )S 2374 0 :M FrMacBegin B 0 FmP F FmOP 182.18 234.166 M (C)S FmE 2375 0 :M f276 sf ( )S 2377 0 :M FrMacBegin B 0 FmP F FmOP 188.85 236.666 M (2)S FmE 2377 0 :M f148 sf ( )S 2379 0 :M FrMacBegin B 0 FmP F FmOP 192.85 234.166 M -0.07( = \(0, 0, 0\), )W FmE 2379 0 :M f203 sf ( )S 2381 0 :M FrMacBegin B 0 FmP F FmOP 239.794 234.166 M (C)S FmE 2382 0 :M f276 sf ( )S 2384 0 :M FrMacBegin B 0 FmP F FmOP 246.464 236.666 M (2)S FmE 2384 0 :M f148 sf ( )S 2386 0 :M FrMacBegin B 0 FmP F FmOP 250.464 234.166 M -0.07([3] = )W FmE 2386 0 :M f203 sf ( )S 2388 0 :M FrMacBegin B 0 FmP F FmOP 272.619 234.166 M (t)S FmE 2389 0 :M f250 sf ( )S 2391 0 :M FrMacBegin B 0 FmP F FmOP 275.397 230.166 M (a)S FmE 2391 0 :M f148 sf ( )S 2393 0 :M FrMacBegin B 0 FmP F FmOP 279.397 234.166 M -0.07([3] \320 1 = 1 \320 1 = 0 and )W FmE 2393 0 :M f203 sf ( )S 2395 0 :M FrMacBegin B 0 FmP F FmOP 371.069 234.166 M (C)S FmE 2396 0 :M f276 sf ( )S 2398 0 :M FrMacBegin B 0 FmP F FmOP 377.739 236.666 M (2)S FmE 2398 0 :M f148 sf ( )S 2400 0 :M FrMacBegin B 0 FmP F FmOP 381.739 234.166 M -0.07([1] )W FmE 2400 0 :M f237 sf ( )S 2402 0 :M FrMacBegin B 0 FmP F FmOP 395.824 234.166 M (\263)S FmE 2403 0 :M f148 sf ( )S 2405 0 :M FrMacBegin B 0 FmP F FmOP 401.313 234.166 M -0.07( )W FmE 2405 0 :M f203 sf ( )S 2407 0 :M FrMacBegin B 0 FmP F FmOP 403.743 234.166 M (t)S FmE 2408 0 :M f250 sf ( )S 2410 0 :M FrMacBegin B 0 FmP F FmOP 406.521 230.166 M (a)S FmE 2410 0 :M f148 sf ( )S 2412 0 :M FrMacBegin B 0 FmP F FmOP 410.521 234.166 M -0.07([1] and )W FmE 2412 0 :M f203 sf ( )S 2414 0 :M FrMacBegin B 0 FmP F FmOP 441.474 234.166 M (C)S FmE 2415 0 :M f276 sf ( )S 2417 0 :M FrMacBegin B 0 FmP F FmOP 448.144 236.666 M (2)S FmE 2417 0 :M f148 sf ( )S 2419 0 :M FrMacBegin B 0 FmP F FmOP 452.144 234.166 M -0.07([2] )W FmE 2419 0 :M f237 sf ( )S 2421 0 :M FrMacBegin B 0 FmP F FmOP 466.23 234.166 M (\263)S FmE 2422 0 :M f148 sf ( )S 2424 0 :M FrMacBegin B 0 FmP F FmOP 471.718 234.166 M -0.07( )W FmE 2424 0 :M f203 sf ( )S 2426 0 :M FrMacBegin B 0 FmP F FmOP 474.148 234.166 M (t)S FmE 2427 0 :M f250 sf ( )S 2429 0 :M FrMacBegin B 0 FmP F FmOP 476.926 230.166 M (a)S FmE 2429 0 :M f148 sf ( )S 2431 0 :M FrMacBegin B 0 FmP F FmOP 480.926 234.166 M -0.07([2] = 0. So )W 58 248 M (the message is accepted, and C)S FmE 2431 0 :M f276 sf ( )S 2433 0 :M FrMacBegin B 0 FmP F FmOP 181.835 250.5 M (2)S FmE 2433 0 :M f148 sf ( )S 2435 0 :M FrMacBegin B 0 FmP F FmOP 185.835 248 M ( is set to \(0, 0, 1\))S FmE 2436 0 :M f203 sf ( )S 2438 0 :M FrMacBegin B 0 FmP F FmOP 58 264.499 M (e)S FmE 2438 0 :M f276 sf ( )S 2440 0 :M FrMacBegin B 0 FmP F FmOP 62.438 266.999 M (22)S FmE 2440 0 :M f148 sf ( )S 2442 0 :M FrMacBegin B 0 FmP F FmOP 70.438 264.499 M (: )S FmE 2443 0 :M f203 sf ( )S 2445 0 :M FrMacBegin B 0 FmP F FmOP 75.717 264.499 M (P)S FmE 2445 0 :M f276 sf ( )S 2447 0 :M FrMacBegin B 0 FmP F FmOP 81.825 266.999 M (2)S FmE 2447 0 :M f148 sf ( )S 2449 0 :M FrMacBegin B 0 FmP F FmOP 85.825 264.499 M ( sends message )S FmE 2450 0 :M f203 sf ( )S 2452 0 :M FrMacBegin B 0 FmP F FmOP 149.414 264.499 M (b)S FmE 2452 0 :M f148 sf ( )S 2454 0 :M FrMacBegin B 0 FmP F FmOP 154.414 264.499 M (; )S FmE 2455 0 :M f203 sf ( )S 2457 0 :M FrMacBegin B 0 FmP F FmOP 159.692 264.499 M (C)S FmE 2457 0 :M f276 sf ( )S 2459 0 :M FrMacBegin B 0 FmP F FmOP 166.362 266.999 M (2)S FmE 2459 0 :M f148 sf ( )S 2461 0 :M FrMacBegin B 0 FmP F FmOP 170.362 264.499 M ( = \(0, 1, 1\); )S FmE 2462 0 :M f203 sf ( )S 2464 0 :M FrMacBegin B 0 FmP F FmOP 217.936 264.499 M (t)S FmE 2464 0 :M f250 sf ( )S 2466 0 :M FrMacBegin B 0 FmP F FmOP 220.714 260.499 M (b)S FmE 2466 0 :M f148 sf ( )S 2468 0 :M FrMacBegin B 0 FmP F FmOP 224.714 264.499 M ( = \(0, 1, 1\))S FmE 2469 0 :M f203 sf ( )S 2471 0 :M FrMacBegin B 0 FmP F FmOP 58 280.999 M (e)S FmE 2471 0 :M f276 sf ( )S 2473 0 :M FrMacBegin B 0 FmP F FmOP 62.438 283.499 M (11)S FmE 2473 0 :M f148 sf ( )S 2475 0 :M FrMacBegin B 0 FmP F FmOP 70.438 280.999 M -0.142(: )W FmE 2476 0 :M f203 sf ( )S 2478 0 :M FrMacBegin B 0 FmP F FmOP 75.575 280.999 M (P)S FmE 2478 0 :M f276 sf ( )S 2480 0 :M FrMacBegin B 0 FmP F FmOP 81.684 283.499 M (1)S FmE 2480 0 :M f148 sf ( )S 2482 0 :M FrMacBegin B 0 FmP F FmOP 85.684 280.999 M -0.142( recei)W -0.251 N (v)S -0.151 N -0.142(es message )W FmE 2483 0 :M f203 sf ( )S 2485 0 :M FrMacBegin B 0 FmP F FmOP 158.977 280.999 M (a)S FmE 2485 0 :M f148 sf ( )S 2487 0 :M FrMacBegin B 0 FmP F FmOP 163.977 280.999 M -0.142(. )W -0.552 N -0.142(As )W FmE 2488 0 :M f203 sf ( )S 2490 0 :M FrMacBegin B 0 FmP F FmOP 184.109 280.999 M (C)S FmE 2490 0 :M f276 sf ( )S 2492 0 :M FrMacBegin B 0 FmP F FmOP 190.779 283.499 M (1)S FmE 2492 0 :M f148 sf ( )S 2494 0 :M FrMacBegin B 0 FmP F FmOP 194.779 280.999 M -0.142( = \(0, 0, 0\), )W FmE 2495 0 :M f203 sf ( )S 2497 0 :M FrMacBegin B 0 FmP F FmOP 241.366 280.999 M (C)S FmE 2497 0 :M f276 sf ( )S 2499 0 :M FrMacBegin B 0 FmP F FmOP 248.036 283.499 M (1)S FmE 2499 0 :M f148 sf ( )S 2501 0 :M FrMacBegin B 0 FmP F FmOP 252.036 280.999 M -0.142([3] = )W FmE 2502 0 :M f203 sf ( )S 2504 0 :M FrMacBegin B 0 FmP F FmOP 274.048 280.999 M (t)S FmE 2504 0 :M f250 sf ( )S 2506 0 :M FrMacBegin B 0 FmP F FmOP 276.826 276.999 M (a)S FmE 2506 0 :M f148 sf ( )S 2508 0 :M FrMacBegin B 0 FmP F FmOP 280.826 280.999 M -0.142([3] \320 1 = 1 \320 1 = 0 and )W FmE 2509 0 :M f203 sf ( )S 2511 0 :M FrMacBegin B 0 FmP F FmOP 371.783 280.999 M (C)S FmE 2511 0 :M f276 sf ( )S 2513 0 :M FrMacBegin B 0 FmP F FmOP 378.453 283.499 M (1)S FmE 2513 0 :M f148 sf ( )S 2515 0 :M FrMacBegin B 0 FmP F FmOP 382.453 280.999 M -0.142([1] )W FmE 2516 0 :M f237 sf ( )S 2518 0 :M FrMacBegin B 0 FmP F FmOP 396.467 280.999 M (\263)S FmE 2518 0 :M f148 sf ( )S 2520 0 :M FrMacBegin B 0 FmP F FmOP 401.955 280.999 M -0.142( )W FmE 2521 0 :M f203 sf ( )S 2523 0 :M FrMacBegin B 0 FmP F FmOP 404.314 280.999 M (t)S FmE 2523 0 :M f250 sf ( )S 2525 0 :M FrMacBegin B 0 FmP F FmOP 407.092 276.999 M (a)S FmE 2525 0 :M f148 sf ( )S 2527 0 :M FrMacBegin B 0 FmP F FmOP 411.092 280.999 M -0.142([1] and )W FmE 2528 0 :M f203 sf ( )S 2530 0 :M FrMacBegin B 0 FmP F FmOP 441.903 280.999 M (C)S FmE 2530 0 :M f276 sf ( )S 2532 0 :M FrMacBegin B 0 FmP F FmOP 448.573 283.499 M (1)S FmE 2532 0 :M f148 sf ( )S 2534 0 :M FrMacBegin B 0 FmP F FmOP 452.573 280.999 M -0.142([2] )W FmE 2535 0 :M f237 sf ( )S 2537 0 :M FrMacBegin B 0 FmP F FmOP 466.586 280.999 M (\263)S FmE 2537 0 :M f148 sf ( )S 2539 0 :M FrMacBegin B 0 FmP F FmOP 472.075 280.999 M -0.142( )W FmE 2540 0 :M f203 sf ( )S 2542 0 :M FrMacBegin B 0 FmP F FmOP 474.433 280.999 M (t)S FmE 2542 0 :M f250 sf ( )S 2544 0 :M FrMacBegin B 0 FmP F FmOP 477.211 276.999 M (a)S FmE 2544 0 :M f148 sf ( )S 2546 0 :M FrMacBegin B 0 FmP F FmOP 481.211 280.999 M -0.142([2] = 0. So )W 58 294.833 M (the message is accepted, and )S FmE 2547 0 :M f203 sf ( )S 2549 0 :M FrMacBegin B 0 FmP F FmOP 175.166 294.833 M (C)S FmE 2549 0 :M f276 sf ( )S 2551 0 :M FrMacBegin B 0 FmP F FmOP 181.835 297.333 M (1)S FmE 2551 0 :M f148 sf ( )S 2553 0 :M FrMacBegin B 0 FmP F FmOP 185.835 294.833 M ( is set to \(0, 0, 1\))S FmE 2554 0 :M f203 sf ( )S 2556 0 :M FrMacBegin B 0 FmP F FmOP 58 311.332 M (e)S FmE 2556 0 :M f276 sf ( )S 2558 0 :M FrMacBegin B 0 FmP F FmOP 62.438 313.832 M (12)S FmE 2558 0 :M f148 sf ( )S 2560 0 :M FrMacBegin B 0 FmP F FmOP 70.438 311.332 M (: )S FmE 2561 0 :M f203 sf ( )S 2563 0 :M FrMacBegin B 0 FmP F FmOP 75.717 311.332 M (P)S FmE 2563 0 :M f276 sf ( )S 2565 0 :M FrMacBegin B 0 FmP F FmOP 81.825 313.832 M (1)S FmE 2565 0 :M f148 sf ( )S 2567 0 :M FrMacBegin B 0 FmP F FmOP 85.825 311.332 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 2568 0 :M f203 sf ( )S 2570 0 :M FrMacBegin B 0 FmP F FmOP 159.543 311.332 M (b)S FmE 2570 0 :M f148 sf ( )S 2572 0 :M FrMacBegin B 0 FmP F FmOP 164.143 311.332 M (. )S -0.552 N (As )S FmE 2573 0 :M f203 sf ( )S 2575 0 :M FrMacBegin B 0 FmP F FmOP 182.2 311.332 M (C)S FmE 2575 0 :M f276 sf ( )S 2577 0 :M FrMacBegin B 0 FmP F FmOP 188.87 313.832 M (1)S FmE 2577 0 :M f148 sf ( )S 2579 0 :M FrMacBegin B 0 FmP F FmOP 192.87 311.332 M ( = \(0, 0, 1\), )S FmE 2580 0 :M f203 sf ( )S 2582 0 :M FrMacBegin B 0 FmP F FmOP 240.165 311.332 M (C)S FmE 2582 0 :M f276 sf ( )S 2584 0 :M FrMacBegin B 0 FmP F FmOP 246.834 313.832 M (1)S FmE 2584 0 :M f148 sf ( )S 2586 0 :M FrMacBegin B 0 FmP F FmOP 250.834 311.332 M ([2] = )S FmE 2587 0 :M f203 sf ( )S 2589 0 :M FrMacBegin B 0 FmP F FmOP 273.129 311.332 M (t)S FmE 2589 0 :M f250 sf ( )S 2591 0 :M FrMacBegin B 0 FmP F FmOP 275.908 307.332 M (b)S FmE 2591 0 :M f148 sf ( )S 2593 0 :M FrMacBegin B 0 FmP F FmOP 279.908 311.332 M ([2] \320 1 = 1\320 1 = 0 and )S FmE 2594 0 :M f203 sf ( )S 2596 0 :M FrMacBegin B 0 FmP F FmOP 369.781 311.332 M (C)S FmE 2596 0 :M f276 sf ( )S 2598 0 :M FrMacBegin B 0 FmP F FmOP 376.451 313.832 M (1)S FmE 2598 0 :M f148 sf ( )S 2600 0 :M FrMacBegin B 0 FmP F FmOP 380.451 311.332 M ([1] )S FmE 2601 0 :M f237 sf ( )S 2603 0 :M FrMacBegin B 0 FmP F FmOP 394.606 311.332 M (\263)S FmE 2603 0 :M f148 sf ( )S 2605 0 :M FrMacBegin B 0 FmP F FmOP 400.094 311.332 M ( )S FmE 2606 0 :M f203 sf ( )S 2608 0 :M FrMacBegin B 0 FmP F FmOP 402.594 311.332 M (t)S FmE 2608 0 :M f250 sf ( )S 2610 0 :M FrMacBegin B 0 FmP F FmOP 405.373 307.332 M (b)S FmE 2610 0 :M f148 sf ( )S 2612 0 :M FrMacBegin B 0 FmP F FmOP 409.373 311.332 M ([1] and )S FmE 2613 0 :M f203 sf ( )S 2615 0 :M FrMacBegin B 0 FmP F FmOP 440.466 311.332 M (C)S FmE 2615 0 :M f276 sf ( )S 2617 0 :M FrMacBegin B 0 FmP F FmOP 447.136 313.832 M (1)S FmE 2617 0 :M f148 sf ( )S 2619 0 :M FrMacBegin B 0 FmP F FmOP 451.136 311.332 M ([3] )S FmE 2620 0 :M f237 sf ( )S 2622 0 :M FrMacBegin B 0 FmP F FmOP 465.292 311.332 M (\263)S FmE 2622 0 :M f148 sf ( )S 2624 0 :M FrMacBegin B 0 FmP F FmOP 470.78 311.332 M ( )S FmE 2625 0 :M f203 sf ( )S 2627 0 :M FrMacBegin B 0 FmP F FmOP 473.28 311.332 M (t)S FmE 2627 0 :M f250 sf ( )S 2629 0 :M FrMacBegin B 0 FmP F FmOP 476.058 307.332 M (b)S FmE 2629 0 :M f148 sf ( )S 2631 0 :M FrMacBegin B 0 FmP F FmOP 480.058 311.332 M ([2] = 0. So )S 58 325.166 M (the message is accepted, and )S FmE 2632 0 :M f203 sf ( )S 2634 0 :M FrMacBegin B 0 FmP F FmOP 175.166 325.166 M (C)S FmE 2634 0 :M f276 sf ( )S 2636 0 :M FrMacBegin B 0 FmP F FmOP 181.835 327.666 M (1)S FmE 2636 0 :M f148 sf ( )S 2638 0 :M FrMacBegin B 0 FmP F FmOP 185.835 325.166 M ( is set to \(0, 1, 1\))S FmE 2639 0 :M f203 sf ( )S 2641 0 :M FrMacBegin B 0 FmP F FmOP 58 341.665 M (e)S FmE 2641 0 :M f276 sf ( )S 2643 0 :M FrMacBegin B 0 FmP F FmOP 62.438 344.165 M (32)S FmE 2643 0 :M f148 sf ( )S 2645 0 :M FrMacBegin B 0 FmP F FmOP 70.438 341.665 M -0.13(: )W FmE 2646 0 :M f203 sf ( )S 2648 0 :M FrMacBegin B 0 FmP F FmOP 75.587 341.665 M (P)S FmE 2648 0 :M f276 sf ( )S 2650 0 :M FrMacBegin B 0 FmP F FmOP 81.695 344.165 M (3)S FmE 2650 0 :M f148 sf ( )S 2652 0 :M FrMacBegin B 0 FmP F FmOP 85.695 341.665 M -0.13( recei)W -0.251 N (v)S -0.151 N -0.13(es message )W FmE 2653 0 :M f203 sf ( )S 2655 0 :M FrMacBegin B 0 FmP F FmOP 159.024 341.665 M (b)S FmE 2655 0 :M f148 sf ( )S 2657 0 :M FrMacBegin B 0 FmP F FmOP 163.624 341.665 M -0.13(. )W -0.552 N -0.13(As )W FmE 2658 0 :M f203 sf ( )S 2660 0 :M FrMacBegin B 0 FmP F FmOP 183.791 341.665 M (C)S FmE 2660 0 :M f276 sf ( )S 2662 0 :M FrMacBegin B 0 FmP F FmOP 190.461 344.165 M (3)S FmE 2662 0 :M f148 sf ( )S 2664 0 :M FrMacBegin B 0 FmP F FmOP 194.461 341.665 M -0.13( = \(0, 0, 1\), )W FmE 2665 0 :M f203 sf ( )S 2667 0 :M FrMacBegin B 0 FmP F FmOP 241.107 341.665 M (C)S FmE 2667 0 :M f276 sf ( )S 2669 0 :M FrMacBegin B 0 FmP F FmOP 247.777 344.165 M (3)S FmE 2669 0 :M f148 sf ( )S 2671 0 :M FrMacBegin B 0 FmP F FmOP 251.777 341.665 M -0.13([2] = )W FmE 2672 0 :M f203 sf ( )S 2674 0 :M FrMacBegin B 0 FmP F FmOP 273.813 341.665 M (t)S FmE 2674 0 :M f250 sf ( )S 2676 0 :M FrMacBegin B 0 FmP F FmOP 276.591 337.665 M (b)S FmE 2676 0 :M f148 sf ( )S 2678 0 :M FrMacBegin B 0 FmP F FmOP 280.591 341.665 M -0.13([2] \320 1 = 1 \320 1 = 1 and )W FmE 2679 0 :M f203 sf ( )S 2681 0 :M FrMacBegin B 0 FmP F FmOP 371.666 341.665 M (C)S FmE 2681 0 :M f276 sf ( )S 2683 0 :M FrMacBegin B 0 FmP F FmOP 378.336 344.165 M (1)S FmE 2683 0 :M f148 sf ( )S 2685 0 :M FrMacBegin B 0 FmP F FmOP 382.336 341.665 M -0.13([1] )W FmE 2686 0 :M f237 sf ( )S 2688 0 :M FrMacBegin B 0 FmP F FmOP 396.362 341.665 M (\263)S FmE 2688 0 :M f148 sf ( )S 2690 0 :M FrMacBegin B 0 FmP F FmOP 401.85 341.665 M -0.13( )W FmE 2691 0 :M f203 sf ( )S 2693 0 :M FrMacBegin B 0 FmP F FmOP 404.22 341.665 M (t)S FmE 2693 0 :M f250 sf ( )S 2695 0 :M FrMacBegin B 0 FmP F FmOP 406.998 337.665 M (b)S FmE 2695 0 :M f148 sf ( )S 2697 0 :M FrMacBegin B 0 FmP F FmOP 410.998 341.665 M -0.13([1] and )W FmE 2698 0 :M f203 sf ( )S 2700 0 :M FrMacBegin B 0 FmP F FmOP 441.833 341.665 M (C)S FmE 2700 0 :M f276 sf ( )S 2702 0 :M FrMacBegin B 0 FmP F FmOP 448.503 344.165 M (1)S FmE 2702 0 :M f148 sf ( )S 2704 0 :M FrMacBegin B 0 FmP F FmOP 452.503 341.665 M -0.13([3] )W FmE 2705 0 :M f237 sf ( )S 2707 0 :M FrMacBegin B 0 FmP F FmOP 466.528 341.665 M (\263)S FmE 2707 0 :M f148 sf ( )S 2709 0 :M FrMacBegin B 0 FmP F FmOP 472.016 341.665 M -0.13( )W FmE 2710 0 :M f203 sf ( )S 2712 0 :M FrMacBegin B 0 FmP F FmOP 474.387 341.665 M (t)S FmE 2712 0 :M f250 sf ( )S 2714 0 :M FrMacBegin B 0 FmP F FmOP 477.165 337.665 M (b)S FmE 2714 0 :M f148 sf ( )S 2716 0 :M FrMacBegin B 0 FmP F FmOP 481.165 341.665 M -0.13([2] = 0. So )W 58 355.499 M (the message is accepted, and )S FmE 2717 0 :M f203 sf ( )S 2719 0 :M FrMacBegin B 0 FmP F FmOP 175.166 355.499 M (C)S FmE 2719 0 :M f276 sf ( )S 2721 0 :M FrMacBegin B 0 FmP F FmOP 181.835 357.999 M (3)S FmE 2721 0 :M f148 sf ( )S 2723 0 :M FrMacBegin B 0 FmP F FmOP 185.835 355.499 M ( is set to \(0, 1, 1\))S 58 383.999 M (No)S -0.251 N (w)S -0.652 N (, suppose )S FmE 2724 0 :M f203 sf ( )S 2726 0 :M FrMacBegin B 0 FmP F FmOP 116.252 383.999 M (t)S FmE 2726 0 :M f250 sf ( )S 2728 0 :M FrMacBegin B 0 FmP F FmOP 119.03 379.999 M (a)S FmE 2728 0 :M f148 sf ( )S 2730 0 :M FrMacBegin B 0 FmP F FmOP 123.03 383.999 M ( arri)S -0.251 N (v)S -0.151 N (ed as e)S -0.251 N (v)S -0.151 N (ent )S FmE 2731 0 :M f203 sf ( )S 2733 0 :M FrMacBegin B 0 FmP F FmOP 190.518 383.999 M (e)S FmE 2733 0 :M f276 sf ( )S 2735 0 :M FrMacBegin B 0 FmP F FmOP 194.957 386.499 M (12)S FmE 2735 0 :M f148 sf ( )S 2737 0 :M FrMacBegin B 0 FmP F FmOP 202.957 383.999 M (, and )S FmE 2738 0 :M f203 sf ( )S 2740 0 :M FrMacBegin B 0 FmP F FmOP 224.895 383.999 M (t)S FmE 2740 0 :M f250 sf ( )S 2742 0 :M FrMacBegin B 0 FmP F FmOP 227.673 379.999 M (b)S FmE 2742 0 :M f148 sf ( )S 2744 0 :M FrMacBegin B 0 FmP F FmOP 231.673 383.999 M ( as e)S -0.251 N (v)S -0.151 N (ent )S FmE 2745 0 :M f203 sf ( )S 2747 0 :M FrMacBegin B 0 FmP F FmOP 268.753 383.999 M (e)S FmE 2747 0 :M f276 sf ( )S 2749 0 :M FrMacBegin B 0 FmP F FmOP 273.192 386.499 M (11)S FmE 2749 0 :M f148 sf ( )S 2751 0 :M FrMacBegin B 0 FmP F FmOP 281.192 383.999 M (:)S 58 520.165 M (Then the progression of time in )S FmE 2752 0 :M f203 sf ( )S 2754 0 :M FrMacBegin B 0 FmP F FmOP 186.293 520.165 M (P)S FmE 2754 0 :M f276 sf ( )S 2756 0 :M FrMacBegin B 0 FmP F FmOP 192.402 522.665 M (1)S FmE 2756 0 :M f148 sf ( )S 2758 0 :M FrMacBegin B 0 FmP F FmOP 196.402 520.165 M ( goes lik)S -0.1 N (e this:)S FmE 2759 0 :M f203 sf ( )S 2761 0 :M FrMacBegin B 0 FmP F FmOP 58 536.665 M (e)S FmE 2761 0 :M f276 sf ( )S 2763 0 :M FrMacBegin B 0 FmP F FmOP 62.438 539.165 M (31)S FmE 2763 0 :M f148 sf ( )S 2765 0 :M FrMacBegin B 0 FmP F FmOP 70.438 536.665 M (: )S FmE 2766 0 :M f203 sf ( )S 2768 0 :M FrMacBegin B 0 FmP F FmOP 75.717 536.665 M (P)S FmE 2768 0 :M f276 sf ( )S 2770 0 :M FrMacBegin B 0 FmP F FmOP 81.825 539.165 M (3)S FmE 2770 0 :M f148 sf ( )S 2772 0 :M FrMacBegin B 0 FmP F FmOP 85.825 536.665 M ( sends message )S FmE 2773 0 :M f203 sf ( )S 2775 0 :M FrMacBegin B 0 FmP F FmOP 149.414 536.665 M (a)S FmE 2775 0 :M f148 sf ( )S 2777 0 :M FrMacBegin B 0 FmP F FmOP 154.414 536.665 M (; )S FmE 2778 0 :M f203 sf ( )S 2780 0 :M FrMacBegin B 0 FmP F FmOP 159.692 536.665 M (C)S FmE 2780 0 :M f276 sf ( )S 2782 0 :M FrMacBegin B 0 FmP F FmOP 166.362 539.165 M (3)S FmE 2782 0 :M f148 sf ( )S 2784 0 :M FrMacBegin B 0 FmP F FmOP 170.362 536.665 M ( = \(0, 0, 1\); )S FmE 2785 0 :M f203 sf ( )S 2787 0 :M FrMacBegin B 0 FmP F FmOP 217.936 536.665 M (t)S FmE 2787 0 :M f250 sf ( )S 2789 0 :M FrMacBegin B 0 FmP F FmOP 220.714 532.665 M (a)S FmE 2789 0 :M f148 sf ( )S 2791 0 :M FrMacBegin B 0 FmP F FmOP 224.714 536.665 M ( = \(0, 0, 1\))S FmE 2792 0 :M f203 sf ( )S 2794 0 :M FrMacBegin B 0 FmP F FmOP 58 553.165 M (e)S FmE 2794 0 :M f276 sf ( )S 2796 0 :M FrMacBegin B 0 FmP F FmOP 62.438 555.665 M (21)S FmE 2796 0 :M f148 sf ( )S 2798 0 :M FrMacBegin B 0 FmP F FmOP 70.438 553.165 M -0.07(: )W FmE 2799 0 :M f203 sf ( )S 2801 0 :M FrMacBegin B 0 FmP F FmOP 75.647 553.165 M (P)S FmE 2801 0 :M f276 sf ( )S 2803 0 :M FrMacBegin B 0 FmP F FmOP 81.755 555.665 M (2)S FmE 2803 0 :M f148 sf ( )S 2805 0 :M FrMacBegin B 0 FmP F FmOP 85.755 553.165 M -0.07( recei)W -0.251 N (v)S -0.151 N -0.07(es message )W FmE 2806 0 :M f203 sf ( )S 2808 0 :M FrMacBegin B 0 FmP F FmOP 159.263 553.165 M (a)S FmE 2808 0 :M f148 sf ( )S 2810 0 :M FrMacBegin B 0 FmP F FmOP 164.263 553.165 M -0.07(. )W -0.552 N -0.07(As )W FmE 2811 0 :M f203 sf ( )S 2813 0 :M FrMacBegin B 0 FmP F FmOP 182.18 553.165 M (C)S FmE 2813 0 :M f276 sf ( )S 2815 0 :M FrMacBegin B 0 FmP F FmOP 188.85 555.665 M (2)S FmE 2815 0 :M f148 sf ( )S 2817 0 :M FrMacBegin B 0 FmP F FmOP 192.85 553.165 M -0.07( = \(0, 0, 0\), )W FmE 2818 0 :M f203 sf ( )S 2820 0 :M FrMacBegin B 0 FmP F FmOP 239.794 553.165 M (C)S FmE 2820 0 :M f276 sf ( )S 2822 0 :M FrMacBegin B 0 FmP F FmOP 246.464 555.665 M (2)S FmE 2822 0 :M f148 sf ( )S 2824 0 :M FrMacBegin B 0 FmP F FmOP 250.464 553.165 M -0.07([3] = )W FmE 2825 0 :M f203 sf ( )S 2827 0 :M FrMacBegin B 0 FmP F FmOP 272.619 553.165 M (t)S FmE 2827 0 :M f250 sf ( )S 2829 0 :M FrMacBegin B 0 FmP F FmOP 275.397 549.165 M (a)S FmE 2829 0 :M f148 sf ( )S 2831 0 :M FrMacBegin B 0 FmP F FmOP 279.397 553.165 M -0.07([3] \320 1 = 1 \320 1 = 0 and )W FmE 2832 0 :M f203 sf ( )S 2834 0 :M FrMacBegin B 0 FmP F FmOP 371.069 553.165 M (C)S FmE 2834 0 :M f276 sf ( )S 2836 0 :M FrMacBegin B 0 FmP F FmOP 377.739 555.665 M (2)S FmE 2836 0 :M f148 sf ( )S 2838 0 :M FrMacBegin B 0 FmP F FmOP 381.739 553.165 M -0.07([1] )W FmE 2839 0 :M f237 sf ( )S 2841 0 :M FrMacBegin B 0 FmP F FmOP 395.824 553.165 M (\263)S FmE 2841 0 :M f148 sf ( )S 2843 0 :M FrMacBegin B 0 FmP F FmOP 401.313 553.165 M -0.07( )W FmE 2844 0 :M f203 sf ( )S 2846 0 :M FrMacBegin B 0 FmP F FmOP 403.743 553.165 M (t)S FmE 2846 0 :M f250 sf ( )S 2848 0 :M FrMacBegin B 0 FmP F FmOP 406.521 549.165 M (a)S FmE 2848 0 :M f148 sf ( )S 2850 0 :M FrMacBegin B 0 FmP F FmOP 410.521 553.165 M -0.07([1] and )W FmE 2851 0 :M f203 sf ( )S 2853 0 :M FrMacBegin B 0 FmP F FmOP 441.474 553.165 M (C)S FmE 2853 0 :M f276 sf ( )S 2855 0 :M FrMacBegin B 0 FmP F FmOP 448.144 555.665 M (2)S FmE 2855 0 :M f148 sf ( )S 2857 0 :M FrMacBegin B 0 FmP F FmOP 452.144 553.165 M -0.07([2] )W FmE 2858 0 :M f237 sf ( )S 2860 0 :M FrMacBegin B 0 FmP F FmOP 466.23 553.165 M (\263)S FmE 2860 0 :M f148 sf ( )S 2862 0 :M FrMacBegin B 0 FmP F FmOP 471.718 553.165 M -0.07( )W FmE 2863 0 :M f203 sf ( )S 2865 0 :M FrMacBegin B 0 FmP F FmOP 474.148 553.165 M (t)S FmE 2865 0 :M f250 sf ( )S 2867 0 :M FrMacBegin B 0 FmP F FmOP 476.926 549.165 M (a)S FmE 2867 0 :M f148 sf ( )S 2869 0 :M FrMacBegin B 0 FmP F FmOP 480.926 553.165 M -0.07([2] = 0. So )W 58 566.998 M (the message is accepted, and C)S FmE 2870 0 :M f276 sf ( )S 2872 0 :M FrMacBegin B 0 FmP F FmOP 181.835 569.498 M (2)S FmE 2872 0 :M f148 sf ( )S 2874 0 :M FrMacBegin B 0 FmP F FmOP 185.835 566.998 M ( is set to \(0, 0, 1\))S FmE 2874 0 :M f203 sf ( )S 2876 0 :M FrMacBegin B 0 FmP F FmOP 58 583.498 M (e)S FmE 2877 0 :M f276 sf ( )S 2879 0 :M FrMacBegin B 0 FmP F FmOP 62.438 585.998 M (22)S FmE 2879 0 :M f148 sf ( )S 2881 0 :M FrMacBegin B 0 FmP F FmOP 70.438 583.498 M (: )S FmE 2881 0 :M f203 sf ( )S 2883 0 :M FrMacBegin B 0 FmP F FmOP 75.717 583.498 M (P)S FmE 2884 0 :M f276 sf ( )S 2886 0 :M FrMacBegin B 0 FmP F FmOP 81.825 585.998 M (2)S FmE 2886 0 :M f148 sf ( )S 2888 0 :M FrMacBegin B 0 FmP F FmOP 85.825 583.498 M ( sends message )S FmE 2888 0 :M f203 sf ( )S 2890 0 :M FrMacBegin B 0 FmP F FmOP 149.414 583.498 M (b)S FmE 2891 0 :M f148 sf ( )S 2893 0 :M FrMacBegin B 0 FmP F FmOP 154.414 583.498 M (; )S FmE 2893 0 :M f203 sf ( )S 2895 0 :M FrMacBegin B 0 FmP F FmOP 159.692 583.498 M (C)S FmE 2896 0 :M f276 sf ( )S 2898 0 :M FrMacBegin B 0 FmP F FmOP 166.362 585.998 M (2)S FmE 2898 0 :M f148 sf ( )S 2900 0 :M FrMacBegin B 0 FmP F FmOP 170.362 583.498 M ( = \(0, 1, 1\); )S FmE 2900 0 :M f203 sf ( )S 2902 0 :M FrMacBegin B 0 FmP F FmOP 217.936 583.498 M (t)S FmE 2903 0 :M f250 sf ( )S 2905 0 :M FrMacBegin B 0 FmP F FmOP 220.714 579.498 M (b)S FmE 2905 0 :M f148 sf ( )S 2907 0 :M FrMacBegin B 0 FmP F FmOP 224.714 583.498 M ( = \(0, 1, 1\))S FmE 2907 0 :M f203 sf ( )S 2909 0 :M FrMacBegin B 0 FmP F FmOP 58 599.998 M (e)S FmE 2910 0 :M f276 sf ( )S 2912 0 :M FrMacBegin B 0 FmP F FmOP 62.438 602.498 M (11)S FmE 2912 0 :M f148 sf ( )S 2914 0 :M FrMacBegin B 0 FmP F FmOP 70.438 599.998 M -0.003(: )W FmE 2914 0 :M f203 sf ( )S 2916 0 :M FrMacBegin B 0 FmP F FmOP 75.713 599.998 M (P)S FmE 2917 0 :M f276 sf ( )S 2919 0 :M FrMacBegin B 0 FmP F FmOP 81.822 602.498 M (1)S FmE 2919 0 :M f148 sf ( )S 2921 0 :M FrMacBegin B 0 FmP F FmOP 85.822 599.998 M -0.003( recei)W -0.251 N (v)S -0.151 N -0.003(es message )W FmE 2921 0 :M f203 sf ( )S 2923 0 :M FrMacBegin B 0 FmP F FmOP 159.53 599.998 M (b)S FmE 2924 0 :M f148 sf ( )S 2926 0 :M FrMacBegin B 0 FmP F FmOP 164.129 599.998 M -0.003(. )W -0.552 N -0.003(As )W FmE 2926 0 :M f203 sf ( )S 2928 0 :M FrMacBegin B 0 FmP F FmOP 182.179 599.998 M (C)S FmE 2929 0 :M f276 sf ( )S 2931 0 :M FrMacBegin B 0 FmP F FmOP 188.849 602.498 M (1)S FmE 2931 0 :M f148 sf ( )S 2933 0 :M FrMacBegin B 0 FmP F FmOP 192.849 599.998 M -0.003( = \(0, 0, 0\), )W FmE 2933 0 :M f203 sf ( )S 2935 0 :M FrMacBegin B 0 FmP F FmOP 240.126 599.998 M (C)S FmE 2936 0 :M f276 sf ( )S 2938 0 :M FrMacBegin B 0 FmP F FmOP 246.796 602.498 M (1)S FmE 2938 0 :M f148 sf ( )S 2940 0 :M FrMacBegin B 0 FmP F FmOP 250.796 599.998 M -0.003([2] = )W FmE 2940 0 :M f203 sf ( )S 2942 0 :M FrMacBegin B 0 FmP F FmOP 273.084 599.998 M (t)S FmE 2943 0 :M f250 sf ( )S 2945 0 :M FrMacBegin B 0 FmP F FmOP 275.862 595.998 M (b)S FmE 2945 0 :M f148 sf ( )S 2947 0 :M FrMacBegin B 0 FmP F FmOP 279.862 599.998 M -0.003([2] \320 1 = 1 \320 1 = 0 and )W FmE 2947 0 :M f203 sf ( )S 2949 0 :M FrMacBegin B 0 FmP F FmOP 372.201 599.998 M (C)S FmE 2950 0 :M f276 sf ( )S 2952 0 :M FrMacBegin B 0 FmP F FmOP 378.871 602.498 M (1)S FmE 2952 0 :M f148 sf ( )S 2954 0 :M FrMacBegin B 0 FmP F FmOP 382.871 599.998 M -0.003([1] )W FmE 2954 0 :M f237 sf ( )S 2956 0 :M FrMacBegin B 0 FmP F FmOP 397.022 599.998 M (\263)S FmE 2957 0 :M f148 sf ( )S 2959 0 :M FrMacBegin B 0 FmP F FmOP 402.511 599.998 M -0.003( )W FmE 2959 0 :M f203 sf ( )S 2961 0 :M FrMacBegin B 0 FmP F FmOP 405.007 599.998 M (t)S FmE 2962 0 :M f250 sf ( )S 2964 0 :M FrMacBegin B 0 FmP F FmOP 407.786 595.998 M (b)S FmE 2964 0 :M f148 sf ( )S 2966 0 :M FrMacBegin B 0 FmP F FmOP 411.786 599.998 M -0.003([1], b)W -0.2 N -0.003(ut )W FmE 2966 0 :M f203 sf ( )S 2968 0 :M FrMacBegin B 0 FmP F FmOP 443.512 599.998 M (C)S FmE 2969 0 :M f276 sf ( )S 2971 0 :M FrMacBegin B 0 FmP F FmOP 450.182 602.498 M (1)S FmE 2971 0 :M f148 sf ( )S 2973 0 :M FrMacBegin B 0 FmP F FmOP 454.182 599.998 M -0.003([3] < )W FmE 2973 0 :M f203 sf ( )S 2975 0 :M FrMacBegin B 0 FmP F FmOP 476.47 599.998 M (t)S FmE 2976 0 :M f250 sf ( )S 2978 0 :M FrMacBegin B 0 FmP F FmOP 479.248 595.998 M (b)S FmE 2978 0 :M f148 sf ( )S 2980 0 :M FrMacBegin B 0 FmP F FmOP 483.248 599.998 M -0.003([3], so the )W 58 613.831 M (message is held until another message arri)S -0.251 N (v)S -0.151 N (es. )S -0.181 N (The v)S -0.151 N (ector clock updating algorithm is not run.)S FmE 2980 0 :M f203 sf ( )S 2982 0 :M FrMacBegin B 0 FmP F FmOP 58 628.497 M (e)S FmE 2983 0 :M f276 sf ( )S 2985 0 :M FrMacBegin B 0 FmP F FmOP 62.438 630.997 M (12)S FmE 2985 0 :M f148 sf ( )S 2987 0 :M FrMacBegin B 0 FmP F FmOP 70.438 628.497 M (: )S FmE 2987 0 :M f203 sf ( )S 2989 0 :M FrMacBegin B 0 FmP F FmOP 75.717 628.497 M (P)S FmE 2990 0 :M f276 sf ( )S 2992 0 :M FrMacBegin B 0 FmP F FmOP 81.825 630.997 M (1)S FmE 2992 0 :M f148 sf ( )S 2994 0 :M FrMacBegin B 0 FmP F FmOP 85.825 628.497 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 2994 0 :M f203 sf ( )S 2996 0 :M FrMacBegin B 0 FmP F FmOP 159.543 628.497 M (a)S FmE 2997 0 :M f148 sf ( )S 2999 0 :M FrMacBegin B 0 FmP F FmOP 164.543 628.497 M (. )S -0.552 N (As )S FmE 2999 0 :M f203 sf ( )S 3001 0 :M FrMacBegin B 0 FmP F FmOP 182.6 628.497 M (C)S FmE 3002 0 :M f276 sf ( )S 3004 0 :M FrMacBegin B 0 FmP F FmOP 189.27 630.997 M (1)S FmE 3004 0 :M f148 sf ( )S 3006 0 :M FrMacBegin B 0 FmP F FmOP 193.27 628.497 M ( = \(0, 0, 0\), )S FmE 3006 0 :M f203 sf ( )S 3008 0 :M FrMacBegin B 0 FmP F FmOP 240.565 628.497 M (C)S FmE 3009 0 :M f276 sf ( )S 3011 0 :M FrMacBegin B 0 FmP F FmOP 247.235 630.997 M (1)S FmE 3011 0 :M f148 sf ( )S 3013 0 :M FrMacBegin B 0 FmP F FmOP 251.235 628.497 M ([3] = )S FmE 3013 0 :M f203 sf ( )S 3015 0 :M FrMacBegin B 0 FmP F FmOP 273.53 628.497 M (t)S FmE 3016 0 :M f250 sf ( )S 3018 0 :M FrMacBegin B 0 FmP F FmOP 276.308 624.498 M (a)S FmE 3018 0 :M f148 sf ( )S 3020 0 :M FrMacBegin B 0 FmP F FmOP 280.308 628.497 M ([3] \320 1 = 1 \320 1 = 0, )S FmE 3020 0 :M f203 sf ( )S 3022 0 :M FrMacBegin B 0 FmP F FmOP 358.243 628.497 M (C)S FmE 3023 0 :M f276 sf ( )S 3025 0 :M FrMacBegin B 0 FmP F FmOP 364.913 630.997 M (1)S FmE 3025 0 :M f148 sf ( )S 3027 0 :M FrMacBegin B 0 FmP F FmOP 368.913 628.497 M ([1] )S FmE 3027 0 :M f237 sf ( )S 3029 0 :M FrMacBegin B 0 FmP F FmOP 383.068 628.497 M (\263)S FmE 3030 0 :M f148 sf ( )S 3032 0 :M FrMacBegin B 0 FmP F FmOP 388.556 628.497 M ( )S FmE 3032 0 :M f203 sf ( )S 3034 0 :M FrMacBegin B 0 FmP F FmOP 391.056 628.497 M (t)S FmE 3035 0 :M f250 sf ( )S 3037 0 :M FrMacBegin B 0 FmP F FmOP 393.834 624.498 M (a)S FmE 3037 0 :M f148 sf ( )S 3039 0 :M FrMacBegin B 0 FmP F FmOP 397.834 628.497 M ([1], and )S FmE 3039 0 :M f203 sf ( )S 3041 0 :M FrMacBegin B 0 FmP F FmOP 431.428 628.497 M (C)S FmE 3042 0 :M f276 sf ( )S 3044 0 :M FrMacBegin B 0 FmP F FmOP 438.098 630.997 M (1)S FmE 3044 0 :M f148 sf ( )S 3046 0 :M FrMacBegin B 0 FmP F FmOP 442.098 628.497 M ([2] )S FmE 3046 0 :M f237 sf ( )S 3048 0 :M FrMacBegin B 0 FmP F FmOP 456.253 628.497 M (\263)S FmE 3049 0 :M f148 sf ( )S 3051 0 :M FrMacBegin B 0 FmP F FmOP 461.742 628.497 M ( )S FmE 3051 0 :M f203 sf ( )S 3053 0 :M FrMacBegin B 0 FmP F FmOP 464.242 628.497 M (t)S FmE 3054 0 :M f250 sf ( )S 3056 0 :M FrMacBegin B 0 FmP F FmOP 467.02 624.498 M (a)S FmE 3056 0 :M f148 sf ( )S 3058 0 :M FrMacBegin B 0 FmP F FmOP 471.02 628.497 M ([2]. )S -0.181 N (The mes-)S 58 644.997 M (sage is accepted and )S FmE 3058 0 :M f203 sf ( )S 3060 0 :M FrMacBegin B 0 FmP F FmOP 141.843 644.997 M (C)S FmE 3061 0 :M f276 sf ( )S 3063 0 :M FrMacBegin B 0 FmP F FmOP 148.513 647.497 M (1)S FmE 3063 0 :M f148 sf ( )S 3065 0 :M FrMacBegin B 0 FmP F FmOP 152.513 644.997 M ( is set to \(0, 0, 1\). No)S -0.251 N (w the queue is check)S -0.1 N (ed. )S -0.552 N (As )S FmE 3065 0 :M f203 sf ( )S 3067 0 :M FrMacBegin B 0 FmP F FmOP 347.378 644.997 M (C)S FmE 3068 0 :M f276 sf ( )S 3070 0 :M FrMacBegin B 0 FmP F FmOP 354.048 647.497 M (1)S FmE 3070 0 :M f148 sf ( )S 3072 0 :M FrMacBegin B 0 FmP F FmOP 358.048 644.997 M ([2] = )S FmE 3072 0 :M f203 sf ( )S 3074 0 :M FrMacBegin B 0 FmP F FmOP 380.343 644.997 M (t)S FmE 3075 0 :M f250 sf ( )S 3077 0 :M FrMacBegin B 0 FmP F FmOP 383.122 640.997 M (b)S FmE 3077 0 :M f148 sf ( )S 3079 0 :M FrMacBegin B 0 FmP F FmOP 387.122 644.997 M ([2] \320 1 = 1 \320 1 = 0, )S FmE 3079 0 :M f203 sf ( )S 3081 0 :M FrMacBegin B 0 FmP F FmOP 465.056 644.997 M (C)S FmE 3082 0 :M f276 sf ( )S 3084 0 :M FrMacBegin B 0 FmP F FmOP 471.726 647.497 M (1)S FmE 3084 0 :M f148 sf ( )S 3086 0 :M FrMacBegin B 0 FmP F FmOP 475.726 644.997 M ([1] )S FmE 3086 0 :M f237 sf ( )S 3088 0 :M FrMacBegin B 0 FmP F FmOP 489.881 644.997 M (\263)S FmE 3089 0 :M f148 sf ( )S 3091 0 :M FrMacBegin B 0 FmP F FmOP 495.37 644.997 M ( )S FmE 3091 0 :M f203 sf ( )S 3093 0 :M FrMacBegin B 0 FmP F FmOP 497.87 644.997 M (t)S FmE 3094 0 :M f250 sf ( )S 3096 0 :M FrMacBegin B 0 FmP F FmOP 500.648 640.997 M (b)S FmE 3096 0 :M f148 sf ( )S 3098 0 :M FrMacBegin B 0 FmP F FmOP 504.648 644.997 M ([1], )S 58 661.497 M (and )S FmE 3098 0 :M f203 sf ( )S 3100 0 :M FrMacBegin B 0 FmP F FmOP 74.938 661.497 M (C)S FmE 3101 0 :M f276 sf ( )S 3103 0 :M FrMacBegin B 0 FmP F FmOP 81.608 663.997 M (1)S FmE 3103 0 :M f148 sf ( )S 3105 0 :M FrMacBegin B 0 FmP F FmOP 85.608 661.497 M ([3] )S FmE 3105 0 :M f237 sf ( )S 3107 0 :M FrMacBegin B 0 FmP F FmOP 99.764 661.497 M (\263)S FmE 3108 0 :M f148 sf ( )S 3110 0 :M FrMacBegin B 0 FmP F FmOP 105.252 661.497 M ( )S FmE 3110 0 :M f203 sf ( )S 3112 0 :M FrMacBegin B 0 FmP F FmOP 107.752 661.497 M (t)S FmE 3113 0 :M f250 sf ( )S 3115 0 :M FrMacBegin B 0 FmP F FmOP 110.53 657.497 M (b)S FmE 3115 0 :M f148 sf ( )S 3117 0 :M FrMacBegin B 0 FmP F FmOP 114.53 661.497 M ([3], that message is accepted and )S FmE 3117 0 :M f203 sf ( )S 3119 0 :M FrMacBegin B 0 FmP F FmOP 248.629 661.497 M (C)S FmE 3120 0 :M f276 sf ( )S 3122 0 :M FrMacBegin B 0 FmP F FmOP 255.299 663.997 M (1)S FmE 3122 0 :M f148 sf ( )S 3124 0 :M FrMacBegin B 0 FmP F FmOP 259.299 661.497 M ( is set to \(0, 1, 1\).)S FmE 3124 0 :M f203 sf ( )S 3126 0 :M FrMacBegin B 0 FmP F FmOP 58 677.997 M (e)S FmE 3127 0 :M f276 sf ( )S 3129 0 :M FrMacBegin B 0 FmP F FmOP 62.438 680.497 M (32)S FmE 3129 0 :M f148 sf ( )S 3131 0 :M FrMacBegin B 0 FmP F FmOP 70.438 677.997 M -0.13(: )W FmE 3131 0 :M f203 sf ( )S 3133 0 :M FrMacBegin B 0 FmP F FmOP 75.587 677.997 M (P)S FmE 3134 0 :M f276 sf ( )S 3136 0 :M FrMacBegin B 0 FmP F FmOP 81.695 680.497 M (3)S FmE 3136 0 :M f148 sf ( )S 3138 0 :M FrMacBegin B 0 FmP F FmOP 85.695 677.997 M -0.13( recei)W -0.251 N (v)S -0.151 N -0.13(es message )W FmE 3138 0 :M f203 sf ( )S 3140 0 :M FrMacBegin B 0 FmP F FmOP 159.024 677.997 M (b)S FmE 3141 0 :M f148 sf ( )S 3143 0 :M FrMacBegin B 0 FmP F FmOP 163.624 677.997 M -0.13(. )W -0.552 N -0.13(As )W FmE 3143 0 :M f203 sf ( )S 3145 0 :M FrMacBegin B 0 FmP F FmOP 183.791 677.997 M (C)S FmE 3146 0 :M f276 sf ( )S 3148 0 :M FrMacBegin B 0 FmP F FmOP 190.461 680.497 M (3)S FmE 3148 0 :M f148 sf ( )S 3150 0 :M FrMacBegin B 0 FmP F FmOP 194.461 677.997 M -0.13( = \(0, 0, 1\), )W FmE 3150 0 :M f203 sf ( )S 3152 0 :M FrMacBegin B 0 FmP F FmOP 241.107 677.997 M (C)S FmE 3153 0 :M f276 sf ( )S 3155 0 :M FrMacBegin B 0 FmP F FmOP 247.777 680.497 M (3)S FmE 3155 0 :M f148 sf ( )S 3157 0 :M FrMacBegin B 0 FmP F FmOP 251.777 677.997 M -0.13([2] = )W FmE 3157 0 :M f203 sf ( )S 3159 0 :M FrMacBegin B 0 FmP F FmOP 273.813 677.997 M (t)S FmE 3160 0 :M f250 sf ( )S 3162 0 :M FrMacBegin B 0 FmP F FmOP 276.591 673.997 M (b)S FmE 3162 0 :M f148 sf ( )S 3164 0 :M FrMacBegin B 0 FmP F FmOP 280.591 677.997 M -0.13([2] \320 1 = 1 \320 1 = 1 and )W FmE 3164 0 :M f203 sf ( )S 3166 0 :M FrMacBegin B 0 FmP F FmOP 371.666 677.997 M (C)S FmE 3167 0 :M f276 sf ( )S 3169 0 :M FrMacBegin B 0 FmP F FmOP 378.336 680.497 M (1)S FmE 3169 0 :M f148 sf ( )S 3171 0 :M FrMacBegin B 0 FmP F FmOP 382.336 677.997 M -0.13([1] )W FmE 3171 0 :M f237 sf ( )S 3173 0 :M FrMacBegin B 0 FmP F FmOP 396.362 677.997 M (\263)S FmE 3174 0 :M f148 sf ( )S 3176 0 :M FrMacBegin B 0 FmP F FmOP 401.85 677.997 M -0.13( )W FmE 3176 0 :M f203 sf ( )S 3178 0 :M FrMacBegin B 0 FmP F FmOP 404.22 677.997 M (t)S FmE 3179 0 :M f250 sf ( )S 3181 0 :M FrMacBegin B 0 FmP F FmOP 406.998 673.997 M (b)S FmE 3181 0 :M f148 sf ( )S 3183 0 :M FrMacBegin B 0 FmP F FmOP 410.998 677.997 M -0.13([1] and )W FmE 3183 0 :M f203 sf ( )S 3185 0 :M FrMacBegin B 0 FmP F FmOP 441.833 677.997 M (C)S FmE 3186 0 :M f276 sf ( )S 3188 0 :M FrMacBegin B 0 FmP F FmOP 448.503 680.497 M (1)S FmE 3188 0 :M f148 sf ( )S 3190 0 :M FrMacBegin B 0 FmP F FmOP 452.503 677.997 M -0.13([3] )W FmE 3190 0 :M f237 sf ( )S 3192 0 :M FrMacBegin B 0 FmP F FmOP 466.528 677.997 M (\263)S FmE 3193 0 :M f148 sf ( )S 3195 0 :M FrMacBegin B 0 FmP F FmOP 472.016 677.997 M -0.13( )W FmE 3195 0 :M f203 sf ( )S 3197 0 :M FrMacBegin B 0 FmP F FmOP 474.387 677.997 M (t)S FmE 3198 0 :M f250 sf ( )S 3200 0 :M FrMacBegin B 0 FmP F FmOP 477.165 673.997 M (b)S FmE 3200 0 :M f148 sf ( )S 3202 0 :M FrMacBegin B 0 FmP F FmOP 481.165 677.997 M -0.13([2] = 0. So )W 58 691.83 M (the message is accepted, and )S FmE 3202 0 :M f203 sf ( )S 3204 0 :M FrMacBegin B 0 FmP F FmOP 175.166 691.83 M (C)S FmE 3205 0 :M f276 sf ( )S 3207 0 :M FrMacBegin B 0 FmP F FmOP 181.835 694.33 M (3)S FmE 3207 0 :M f148 sf ( )S 3209 0 :M FrMacBegin B 0 FmP F FmOP 185.835 691.83 M ( is set to \(0, 1, 1\))S FmE 58 72 468 118 rC 3209 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP 112 90.804 FmB 378 0 FmL 2 1 FmSo 111.333 126.804 FmB 378 0 FmL 2 1 FmSo 112 171.804 FmB 378 0 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 259.5 90.971 FmAF T 0 360 4.5 4.5 0 259.5 90.971 2 1 F FmAP 0 360 4.5 4.5 0 T 200.833 126.971 FmAF T 0 360 4.5 4.5 0 200.833 126.971 2 1 F FmAP 0 360 4.5 4.5 0 T 251.5 126.971 FmAF T 0 360 4.5 4.5 0 251.5 126.971 2 1 F FmAP 0 360 4.5 4.5 0 T 163.5 172.971 FmAF T 0 360 4.5 4.5 0 163.5 172.971 2 1 F FmAP 0 360 4.5 4.5 0 T 439.5 172.304 FmAF T 0 360 4.5 4.5 0 439.5 172.304 2 1 F FmAP 0 360 4.5 4.5 0 T 436.833 91.637 FmAF T 0 360 4.5 4.5 0 436.833 91.637 2 1 F FmAP FmE 3209 0 :M f289 sf ( )S 3212 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP 91.333 91.171 M (P)S FmE 3212 0 :M f148 sf ( )S 3214 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 94.171 M 0.96 0.96 scale (1)S FmR FmE 3215 0 :M f289 sf ( )S 3218 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP 91.333 128.505 M (P)S FmE 3218 0 :M f148 sf ( )S 3220 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 131.505 M 0.96 0.96 scale (2)S FmR FmE 3220 0 :M f289 sf ( )S 3223 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP 91.333 175.171 M (P)S FmE 3223 0 :M f148 sf ( )S 3225 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 178.171 M 0.96 0.96 scale (3)S FmR FmG 258.126 80.917 M 0.96 0.96 scale (e11)S FmR FmG 198.667 119.504 M 0.96 0.96 scale (e21)S FmR FmG 252 119.504 M 0.96 0.96 scale (e22)S FmR FmG 147.333 164.171 M 0.96 0.96 scale (e31)S FmR FmG 438 164.838 M 0.96 0.96 scale (e32)S FmR FmG 430.667 84.171 M 0.96 0.96 scale (e12)S FmR 418.972 94.976 FmB -0.616 -3.416 FmL 12.529 1.266 FmL -11.296 5.565 FmL 1 FmS 418.972 94.976 FmB -0.616 -3.416 FmL 12.529 1.266 FmL -11.296 5.565 FmL FmFl 255.333 124.504 FmB 163.146 -29.44 FmL 2 1 FmSo 421.734 165.548 FmB 0.737 -3.392 FmL 11.091 5.963 FmL -12.566 0.82 FmL 1 FmS 421.734 165.548 FmB 0.737 -3.392 FmL 11.091 5.963 FmL -12.566 0.82 FmL FmFl 253.333 128.934 FmB 167.912 36.507 FmL 2 1 FmSo 190.319 140.443 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL 1 FmS 190.319 140.443 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL FmFl 165.333 169.838 FmB 24.662 -29.014 FmL 2 1 FmSo 247.333 101.876 FmB -2.23 -2.66 FmL 11.506 -5.116 FmL -7.047 10.436 FmL 1 FmS 247.333 101.876 FmB -2.23 -2.66 FmL 11.506 -5.116 FmL -7.047 10.436 FmL FmFl 167.333 168.934 FmB 79.617 -66.738 FmL 2 1 FmSo FmE 3226 0 :M f203 sf ( )S 3228 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP 178.667 167.235 M (a)S 253.333 139.902 M (b)S FmE gR gS 58 389 468 118 rC 3228 0 :M FrMacBegin 58 389.165 468 117.333 FmKp B 0 FmP F FmOP 112 407.969 FmB 378 0 FmL 2 1 FmSo 111.333 443.969 FmB 378 0 FmL 2 1 FmSo 112 488.969 FmB 378 0 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 281.167 408.332 FmAF T 0 360 4.5 4.5 0 281.167 408.332 2 1 F FmAP 0 360 4.5 4.5 0 T 200.833 444.136 FmAF T 0 360 4.5 4.5 0 200.833 444.136 2 1 F FmAP 0 360 4.5 4.5 0 T 251.5 444.136 FmAF T 0 360 4.5 4.5 0 251.5 444.136 2 1 F FmAP 0 360 4.5 4.5 0 T 163.5 490.136 FmAF T 0 360 4.5 4.5 0 163.5 490.136 2 1 F FmAP 0 360 4.5 4.5 0 T 439.5 489.469 FmAF T 0 360 4.5 4.5 0 439.5 489.469 2 1 F FmAP 0 360 4.5 4.5 0 T 436.833 408.802 FmAF T 0 360 4.5 4.5 0 436.833 408.802 2 1 F FmAP FmE 3228 0 :M f289 sf ( )S 3231 0 :M FrMacBegin 58 389.165 468 117.333 FmKp B 0 FmP F FmOP 91.333 408.336 M (P)S FmE 3231 0 :M f148 sf ( )S 3233 0 :M FrMacBegin 58 389.165 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 411.336 M 0.96 0.96 scale (1)S FmR FmE 3234 0 :M f289 sf ( )S 3237 0 :M FrMacBegin 58 389.165 468 117.333 FmKp B 0 FmP F FmOP 91.333 445.67 M (P)S FmE 3237 0 :M f148 sf ( )S 3239 0 :M FrMacBegin 58 389.165 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 448.67 M 0.96 0.96 scale (2)S FmR FmE 3239 0 :M f289 sf ( )S 3242 0 :M FrMacBegin 58 389.165 468 117.333 FmKp B 0 FmP F FmOP 91.333 492.336 M (P)S FmE 3242 0 :M f148 sf ( )S 3244 0 :M FrMacBegin 58 389.165 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 495.336 M 0.96 0.96 scale (3)S FmR FmG 279.792 398.278 M 0.96 0.96 scale (e11)S FmR FmG 198.667 436.67 M 0.96 0.96 scale (e21)S FmR FmG 236.667 434.67 M 0.96 0.96 scale (e22)S FmR FmG 147.333 481.336 M 0.96 0.96 scale (e31)S FmR FmG 438 482.003 M 0.96 0.96 scale (e32)S FmR FmG 430.667 401.336 M 0.96 0.96 scale (e12)S FmR 271.222 421.3 FmB -2.693 -2.189 FmL 10.328 -7.204 FmL -4.941 11.583 FmL 1 FmS 271.222 421.3 FmB -2.693 -2.189 FmL 10.328 -7.204 FmL -4.941 11.583 FmL FmFl 254.667 441.67 FmB 16.24 -19.982 FmL 2 1 FmSo 421.734 482.713 FmB 0.737 -3.392 FmL 11.091 5.963 FmL -12.566 0.82 FmL 1 FmS 421.734 482.713 FmB 0.737 -3.392 FmL 11.091 5.963 FmL -12.566 0.82 FmL FmFl 253.333 446.1 FmB 167.912 36.507 FmL 2 1 FmSo 190.319 457.608 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL 1 FmS 190.319 457.608 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL FmFl 165.333 487.003 FmB 24.662 -29.014 FmL 2 1 FmSo 419.945 414.304 FmB -0.949 -3.339 FmL 12.593 0.03 FmL -10.695 6.648 FmL 1 FmS 419.945 414.304 FmB -0.949 -3.339 FmL 12.593 0.03 FmL -10.695 6.648 FmL FmFl 167.333 486.1 FmB 252.131 -71.659 FmL 2 1 FmSo FmE 3245 0 :M f203 sf ( )S 3247 0 :M FrMacBegin 58 389.165 468 117.333 FmKp B 0 FmP F FmOP 181.333 477.166 M (a)S 269.333 439.166 M (b)S FmE endp showpage %%PageTrailer %%Page: 6 6 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 6 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 3247 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 3247 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 3247 0 :M f148 sf ( )S 3249 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Schiper-Eggli-Sandoz Protocol)S 61.271 N (ECS 251 \320 Winter 2001)S 159.015 N (Page )S (6)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 3250 0 :M f175 sf ( )S 3254 0 :M FrMacBegin B 0 FmP F FmOP 174.253 72 M (Schiper)S -0.668 N (-Eggli-Sandoz Pr)S -0.325 N (otocol)S FmE 3254 0 :M f263 sf ( )S 3257 0 :M FrMacBegin B 0 FmP F FmOP 58 104 M (Intr)S -0.217 N (oduction)S FmE 3257 0 :M f148 sf ( )S 3259 0 :M FrMacBegin B 0 FmP F FmOP 58 121.667 M (The goal of this protocol is to ensure that messages are gi)S -0.251 N (v)S -0.151 N (en to the recei)S -0.251 N (ving processes in order of sending. Unlik)S -0.1 N (e )S 58 133.667 M (the Birman-Schiper)S -0.2 N (-Stephenson protocol, it does not require using broadcast messages. Each message has an associ-)S 58 145.667 M -0.353(ated v)W -0.151 N -0.353(ector that contains information for the recipient to determine if another message preceded it. Clocks are updated )W 58 157.667 M (only when messages are sent.)S FmE 3260 0 :M f263 sf ( )S 3263 0 :M FrMacBegin B 0 FmP F FmOP 58 183 M (Notation)S FmE 3263 0 :M f148 sf ( )S 3265 0 :M FrMacBegin B 0 FmP F FmOP 58 200.667 M (\245)S FmE 3265 0 :M f203 sf ( )S 3267 0 :M FrMacBegin B 0 FmP F FmOP 76 200.667 M (n)S FmE 3268 0 :M f148 sf ( )S 3270 0 :M FrMacBegin B 0 FmP F FmOP 81 200.667 M ( processes)S 58 212.667 M (\245)S FmE 3270 0 :M f203 sf ( )S 3272 0 :M FrMacBegin B 0 FmP F FmOP 76 212.667 M (P)S FmE 3273 0 :M f250 sf ( )S 3275 0 :M FrMacBegin B 0 FmP F FmOP 82.108 215.167 M (i)S FmE 3275 0 :M f148 sf ( )S 3277 0 :M FrMacBegin B 0 FmP F FmOP 84.331 212.667 M ( process)S 58 226.5 M (\245)S FmE 3277 0 :M f203 sf ( )S 3279 0 :M FrMacBegin B 0 FmP F FmOP 76 226.5 M (C)S FmE 3280 0 :M f250 sf ( )S 3282 0 :M FrMacBegin B 0 FmP F FmOP 82.67 229 M (i)S FmE 3282 0 :M f148 sf ( )S 3284 0 :M FrMacBegin B 0 FmP F FmOP 84.893 226.5 M -0.013(. v)W -0.151 N -0.013(ector clock associated with process )W FmE 3284 0 :M f203 sf ( )S 3286 0 :M FrMacBegin B 0 FmP F FmOP 237.65 226.5 M (P)S FmE 3287 0 :M f250 sf ( )S 3289 0 :M FrMacBegin B 0 FmP F FmOP 243.759 229 M (i)S FmE 3289 0 :M f148 sf ( )S 3291 0 :M FrMacBegin B 0 FmP F FmOP 245.981 226.5 M -0.013(; )W FmE 3291 0 :M f203 sf ( )S 3293 0 :M FrMacBegin B 0 FmP F FmOP 251.247 226.5 M (j)S FmE 3294 0 :M f148 sf ( )S 3296 0 :M FrMacBegin B 0 FmP F FmOP 254.025 226.5 M -0.013(th element is )W FmE 3296 0 :M f203 sf ( )S 3298 0 :M FrMacBegin B 0 FmP F FmOP 307.583 226.5 M (C)S FmE 3299 0 :M f250 sf ( )S 3301 0 :M FrMacBegin B 0 FmP F FmOP 314.253 229 M (i)S FmE 3301 0 :M f148 sf ( )S 3303 0 :M FrMacBegin B 0 FmP F FmOP 316.476 226.5 M ([)S FmE 3303 0 :M f203 sf ( )S 3305 0 :M FrMacBegin B 0 FmP F FmOP 319.803 226.5 M (j)S FmE 3306 0 :M f148 sf ( )S 3308 0 :M FrMacBegin B 0 FmP F FmOP 322.582 226.5 M -0.013(] and contains )W FmE 3308 0 :M f203 sf ( )S 3310 0 :M FrMacBegin B 0 FmP F FmOP 381.132 226.5 M (P)S FmE 3311 0 :M f250 sf ( )S 3313 0 :M FrMacBegin B 0 FmP F FmOP 387.241 229 M (i)S FmE 3313 0 :M f148 sf ( )S 3315 0 :M FrMacBegin B 0 FmP F FmOP 389.463 226.5 M (\325)S -0.552 N -0.013(s latest v)W -0.251 N -0.013(alue for the current time )W 76 240.333 M (in process )S FmE 3315 0 :M f203 sf ( )S 3317 0 :M FrMacBegin B 0 FmP F FmOP 118.761 240.333 M (P)S FmE 3318 0 :M f250 sf ( )S 3320 0 :M FrMacBegin B 0 FmP F FmOP 124.87 242.833 M (k)S FmE 3320 0 :M f148 sf ( )S 3322 0 :M FrMacBegin B 0 FmP F FmOP 128.42 240.333 M (.)S 58 256.833 M (\245)S FmE 3322 0 :M f203 sf ( )S 3324 0 :M FrMacBegin B 0 FmP F FmOP 76 256.833 M (t)S FmE 3325 0 :M f250 sf ( )S 3327 0 :M FrMacBegin B 0 FmP F FmOP 78.778 252.833 M (m)S FmE 3327 0 :M f148 sf ( )S 3329 0 :M FrMacBegin B 0 FmP F FmOP 84.556 256.833 M ( v)S -0.151 N (ector timestamp for message )S FmE 3329 0 :M f203 sf ( )S 3331 0 :M FrMacBegin B 0 FmP F FmOP 209.072 256.833 M (m)S FmE 3332 0 :M f148 sf ( )S 3334 0 :M FrMacBegin B 0 FmP F FmOP 216.292 256.833 M ( \(stamped )S FmE 3334 0 :M f203 sf ( )S 3336 0 :M FrMacBegin B 0 FmP F FmOP 257.942 256.833 M (after)S FmE 3337 0 :M f148 sf ( )S 3339 0 :M FrMacBegin B 0 FmP F FmOP 276.826 256.833 M ( local clock is incremented\))S 58 271.499 M (\245)S FmE 3339 0 :M f203 sf ( )S 3341 0 :M FrMacBegin B 0 FmP F FmOP 76 271.499 M (t)S FmE 3342 0 :M f250 sf ( )S 3344 0 :M FrMacBegin B 0 FmP F FmOP 78.778 267.5 M (i)S FmE 3344 0 :M f148 sf ( )S 3346 0 :M FrMacBegin B 0 FmP F FmOP 81.001 271.499 M ( current time at process )S FmE 3346 0 :M f203 sf ( )S 3348 0 :M FrMacBegin B 0 FmP F FmOP 176.785 271.499 M (P)S FmE 3349 0 :M f250 sf ( )S 3351 0 :M FrMacBegin B 0 FmP F FmOP 182.893 273.999 M (i)S FmE 3351 0 :M f148 sf ( )S 3353 0 :M FrMacBegin B 0 FmP F FmOP 58 287.999 M (\245)S FmE 3353 0 :M f203 sf ( )S 3355 0 :M FrMacBegin B 0 FmP F FmOP 76 287.999 M (V)S FmE 3356 0 :M f250 sf ( )S 3358 0 :M FrMacBegin B 0 FmP F FmOP 81.515 290.499 M (i)S FmE 3358 0 :M f148 sf ( )S 3360 0 :M FrMacBegin B 0 FmP F FmOP 83.737 287.999 M ( v)S -0.151 N (ector of )S FmE 3360 0 :M f203 sf ( )S 3362 0 :M FrMacBegin B 0 FmP F FmOP 124.397 287.999 M (P)S FmE 3363 0 :M f250 sf ( )S 3365 0 :M FrMacBegin B 0 FmP F FmOP 130.505 290.499 M (i)S FmE 3365 0 :M f148 sf ( )S 3367 0 :M FrMacBegin B 0 FmP F FmOP 132.728 287.999 M (\325)S -0.552 N (s pre)S -0.251 N (viously sent messages; )S FmE 3367 0 :M f203 sf ( )S 3369 0 :M FrMacBegin B 0 FmP F FmOP 247.647 287.999 M (V)S FmE 3370 0 :M f250 sf ( )S 3372 0 :M FrMacBegin B 0 FmP F FmOP 253.162 290.499 M (i)S FmE 3372 0 :M f148 sf ( )S 3374 0 :M FrMacBegin B 0 FmP F FmOP 255.384 287.999 M ([)S FmE 3374 0 :M f203 sf ( )S 3376 0 :M FrMacBegin B 0 FmP F FmOP 258.712 287.999 M (j)S FmE 3377 0 :M f148 sf ( )S 3379 0 :M FrMacBegin B 0 FmP F FmOP 261.49 287.999 M (] = )S FmE 3379 0 :M f203 sf ( )S 3381 0 :M FrMacBegin B 0 FmP F FmOP 275.458 287.999 M (t)S FmE 3382 0 :M f250 sf ( )S 3384 0 :M FrMacBegin B 0 FmP F FmOP 278.236 283.999 M (m)S FmE 3384 0 :M f148 sf ( )S 3386 0 :M FrMacBegin B 0 FmP F FmOP 284.013 287.999 M (, where the last message sent to )S FmE 3386 0 :M f203 sf ( )S 3388 0 :M FrMacBegin B 0 FmP F FmOP 412.294 287.999 M (P)S FmE 3389 0 :M f250 sf ( )S 3391 0 :M FrMacBegin B 0 FmP F FmOP 418.403 290.499 M (j)S FmE 3391 0 :M f148 sf ( )S 3393 0 :M FrMacBegin B 0 FmP F FmOP 420.626 287.999 M ( has the v)S -0.151 N (ector timestamp )S FmE 3393 0 :M f203 sf ( )S 3395 0 :M FrMacBegin B 0 FmP F FmOP 76 304.499 M (t)S FmE 3396 0 :M f250 sf ( )S 3398 0 :M FrMacBegin B 0 FmP F FmOP 78.778 300.499 M (m)S FmE 3398 0 :M f148 sf ( )S 3400 0 :M FrMacBegin B 0 FmP F FmOP 84.556 304.499 M (; )S FmE 3400 0 :M f203 sf ( )S 3402 0 :M FrMacBegin B 0 FmP F FmOP 89.482 304.499 M (V)S FmE 3403 0 :M f250 sf ( )S 3405 0 :M FrMacBegin B 0 FmP F FmOP 94.997 306.999 M (i)S FmE 3405 0 :M f148 sf ( )S 3407 0 :M FrMacBegin B 0 FmP F FmOP 97.22 304.499 M ([)S FmE 3407 0 :M f203 sf ( )S 3409 0 :M FrMacBegin B 0 FmP F FmOP 100.547 304.499 M (j)S FmE 3410 0 :M f148 sf ( )S 3412 0 :M FrMacBegin B 0 FmP F FmOP 103.326 304.499 M (][)S FmE 3412 0 :M f203 sf ( )S 3414 0 :M FrMacBegin B 0 FmP F FmOP 109.981 304.499 M (k)S FmE 3415 0 :M f148 sf ( )S 3417 0 :M FrMacBegin B 0 FmP F FmOP 114.419 304.499 M (] is the )S FmE 3417 0 :M f203 sf ( )S 3419 0 :M FrMacBegin B 0 FmP F FmOP 144.131 304.499 M (k)S FmE 3420 0 :M f148 sf ( )S 3422 0 :M FrMacBegin B 0 FmP F FmOP 148.57 304.499 M (th component of )S FmE 3422 0 :M f203 sf ( )S 3424 0 :M FrMacBegin B 0 FmP F FmOP 216.258 304.499 M (V)S FmE 3425 0 :M f250 sf ( )S 3427 0 :M FrMacBegin B 0 FmP F FmOP 221.772 306.999 M (i)S FmE 3427 0 :M f148 sf ( )S 3429 0 :M FrMacBegin B 0 FmP F FmOP 223.995 304.499 M ([)S FmE 3429 0 :M f203 sf ( )S 3431 0 :M FrMacBegin B 0 FmP F FmOP 227.323 304.499 M (j)S FmE 3432 0 :M f148 sf ( )S 3434 0 :M FrMacBegin B 0 FmP F FmOP 230.101 304.499 M (].)S 58 320.999 M (\245)S FmE 3434 0 :M f203 sf ( )S 3436 0 :M FrMacBegin B 0 FmP F FmOP 76 320.999 M (V)S FmE 3437 0 :M f250 sf ( )S 3439 0 :M FrMacBegin B 0 FmP F FmOP 82.108 316.999 M (m)S FmE 3439 0 :M f148 sf ( )S 3441 0 :M FrMacBegin B 0 FmP F FmOP 87.886 320.999 M ( v)S -0.151 N (ector accompan)S -0.151 N (ying message )S FmE 3441 0 :M f203 sf ( )S 3443 0 :M FrMacBegin B 0 FmP F FmOP 214.749 320.999 M (m)S FmE 3444 0 :M f263 sf ( )S 3447 0 :M FrMacBegin B 0 FmP F FmOP 58 346.332 M (Pr)S -0.217 N (otocol)S FmE 3447 0 :M f319 sf ( )S 3449 0 :M FrMacBegin B 0 FmP F FmOP 58 363.999 M (P)S FmE 3449 0 :M f332 sf ( )S 3451 0 :M FrMacBegin B 0 FmP F FmOP 64.108 366.499 M (i)S FmE 3451 0 :M f345 sf ( )S 3453 0 :M FrMacBegin B 0 FmP F FmOP 66.331 363.999 M ( sends a message to )S FmE 3454 0 :M f319 sf ( )S 3456 0 :M FrMacBegin B 0 FmP F FmOP 150.477 363.999 M (P)S FmE 3456 0 :M f332 sf ( )S 3458 0 :M FrMacBegin B 0 FmP F FmOP 156.585 366.499 M (j)S FmE 3458 0 :M f148 sf ( )S 3460 0 :M FrMacBegin B 0 FmP F FmOP 58 380.499 M (1.)S FmE 3461 0 :M f203 sf ( )S 3463 0 :M FrMacBegin B 0 FmP F FmOP 76 380.499 M (P)S FmE 3463 0 :M f250 sf ( )S 3465 0 :M FrMacBegin B 0 FmP F FmOP 82.108 382.999 M (i)S FmE 3465 0 :M f148 sf ( )S 3467 0 :M FrMacBegin B 0 FmP F FmOP 84.331 380.499 M ( sends message )S FmE 3468 0 :M f203 sf ( )S 3470 0 :M FrMacBegin B 0 FmP F FmOP 147.92 380.499 M (m)S FmE 3470 0 :M f148 sf ( )S 3472 0 :M FrMacBegin B 0 FmP F FmOP 155.139 380.499 M (, timestamped )S FmE 3473 0 :M f203 sf ( )S 3475 0 :M FrMacBegin B 0 FmP F FmOP 213.735 380.499 M (t)S FmE 3475 0 :M f250 sf ( )S 3477 0 :M FrMacBegin B 0 FmP F FmOP 216.514 376.499 M (m)S FmE 3477 0 :M f148 sf ( )S 3479 0 :M FrMacBegin B 0 FmP F FmOP 222.291 380.499 M (, and )S FmE 3480 0 :M f203 sf ( )S 3482 0 :M FrMacBegin B 0 FmP F FmOP 243.878 380.499 M (V)S FmE 3482 0 :M f250 sf ( )S 3484 0 :M FrMacBegin B 0 FmP F FmOP 249.393 382.999 M (i)S FmE 3484 0 :M f148 sf ( )S 3486 0 :M FrMacBegin B 0 FmP F FmOP 251.615 380.499 M (, to process )S FmE 3487 0 :M f203 sf ( )S 3489 0 :M FrMacBegin B 0 FmP F FmOP 299.376 380.499 M (P)S FmE 3489 0 :M f250 sf ( )S 3491 0 :M FrMacBegin B 0 FmP F FmOP 305.485 382.999 M (j)S FmE 3491 0 :M f148 sf ( )S 3493 0 :M FrMacBegin B 0 FmP F FmOP 307.708 380.499 M ( .)S 58 397.299 M (2.)S FmE 3494 0 :M f203 sf ( )S 3496 0 :M FrMacBegin B 0 FmP F FmOP 76 397.299 M (P)S FmE 3496 0 :M f250 sf ( )S 3498 0 :M FrMacBegin B 0 FmP F FmOP 82.108 399.799 M (i)S FmE 3498 0 :M f148 sf ( )S 3500 0 :M FrMacBegin B 0 FmP F FmOP 84.331 397.299 M ( sets )S FmE 3501 0 :M f203 sf ( )S 3503 0 :M FrMacBegin B 0 FmP F FmOP 103.975 397.299 M (V)S FmE 3503 0 :M f250 sf ( )S 3505 0 :M FrMacBegin B 0 FmP F FmOP 109.489 399.799 M (i)S FmE 3505 0 :M f148 sf ( )S 3507 0 :M FrMacBegin B 0 FmP F FmOP 111.712 397.299 M ([)S FmE 3508 0 :M f203 sf ( )S 3510 0 :M FrMacBegin B 0 FmP F FmOP 115.04 397.299 M (j)S FmE 3510 0 :M f148 sf ( )S 3512 0 :M FrMacBegin B 0 FmP F FmOP 117.818 397.299 M (] )S FmE 3513 0 :M f237 sf ( )S 3515 0 :M FrMacBegin B 0 FmP F FmOP 123.646 397.299 M (\254)S FmE 3515 0 :M f148 sf ( )S 3517 0 :M FrMacBegin B 0 FmP F FmOP 133.514 397.299 M ( )S FmE 3518 0 :M f203 sf ( )S 3520 0 :M FrMacBegin B 0 FmP F FmOP 136.014 397.299 M (t)S FmE 3520 0 :M f250 sf ( )S 3522 0 :M FrMacBegin B 0 FmP F FmOP 138.792 393.299 M (m)S FmE 3522 0 :M f148 sf ( )S 3524 0 :M FrMacBegin B 0 FmP F FmOP 144.569 397.299 M (.)S FmE 3525 0 :M f319 sf ( )S 3527 0 :M FrMacBegin B 0 FmP F FmOP 58 411.432 M (P)S FmE 3527 0 :M f332 sf ( )S 3529 0 :M FrMacBegin B 0 FmP F FmOP 64.108 413.932 M (j)S FmE 3529 0 :M f345 sf ( )S 3531 0 :M FrMacBegin B 0 FmP F FmOP 66.331 411.432 M ( r)S -0.181 N (ecei)S -0.1 N (v)S -0.1 N (es a message fr)S -0.181 N (om )S FmE 3532 0 :M f319 sf ( )S 3534 0 :M FrMacBegin B 0 FmP F FmOP 173.206 411.432 M (P)S FmE 3534 0 :M f332 sf ( )S 3536 0 :M FrMacBegin B 0 FmP F FmOP 179.314 413.932 M (i)S FmE 3536 0 :M f148 sf ( )S 3538 0 :M FrMacBegin B 0 FmP F FmOP 58 425.265 M (1.)S 10.5 N (When )S FmE 3539 0 :M f203 sf ( )S 3541 0 :M FrMacBegin B 0 FmP F FmOP 102.377 425.265 M (P)S FmE 3541 0 :M f250 sf ( )S 3543 0 :M FrMacBegin B 0 FmP F FmOP 108.485 427.765 M (j)S FmE 3543 0 :M f148 sf ( )S 3545 0 :M FrMacBegin B 0 FmP F FmOP 110.708 425.265 M (, )S FmE 3546 0 :M f203 sf ( )S 3548 0 :M FrMacBegin B 0 FmP F FmOP 115.708 425.265 M (j)S FmE 3548 0 :M f148 sf ( )S 3550 0 :M FrMacBegin B 0 FmP F FmOP 118.486 425.265 M ( )S FmE 3551 0 :M f237 sf ( )S 3553 0 :M FrMacBegin B 0 FmP F FmOP 120.986 425.265 M (\271)S FmE 3553 0 :M f148 sf ( )S 3555 0 :M FrMacBegin B 0 FmP F FmOP 126.475 425.265 M ( )S FmE 3556 0 :M f203 sf ( )S 3558 0 :M FrMacBegin B 0 FmP F FmOP 128.975 425.265 M (i)S FmE 3558 0 :M f148 sf ( )S 3560 0 :M FrMacBegin B 0 FmP F FmOP 131.753 425.265 M (, recei)S -0.251 N (v)S -0.151 N (es )S FmE 3561 0 :M f203 sf ( )S 3563 0 :M FrMacBegin B 0 FmP F FmOP 171.599 425.265 M (m)S FmE 3563 0 :M f148 sf ( )S 3565 0 :M FrMacBegin B 0 FmP F FmOP 178.818 425.265 M (, it delays the message\325)S -0.552 N (s deli)S -0.251 N (v)S -0.151 N (ery if )S FmE 3566 0 :M f203 sf ( )S 3568 0 :M FrMacBegin B 0 FmP F FmOP 321.138 425.265 M (both)S FmE 3568 0 :M f148 sf ( )S 3570 0 :M FrMacBegin B 0 FmP F FmOP 338.916 425.265 M (:)S 76 441.765 M (a.)S FmE 3571 0 :M f203 sf ( )S 3573 0 :M FrMacBegin B 0 FmP F FmOP 94 441.765 M (V)S FmE 3573 0 :M f250 sf ( )S 3575 0 :M FrMacBegin B 0 FmP F FmOP 100.108 437.765 M (m)S FmE 3575 0 :M f148 sf ( )S 3577 0 :M FrMacBegin B 0 FmP F FmOP 105.886 441.765 M ([)S FmE 3578 0 :M f203 sf ( )S 3580 0 :M FrMacBegin B 0 FmP F FmOP 109.213 441.765 M (j)S FmE 3580 0 :M f148 sf ( )S 3582 0 :M FrMacBegin B 0 FmP F FmOP 111.992 441.765 M (] is set; and)S 76 456.431 M (b)S -0.4 N (.)S FmE 3583 0 :M f203 sf ( )S 3585 0 :M FrMacBegin B 0 FmP F FmOP 94 456.431 M (V)S FmE 3585 0 :M f250 sf ( )S 3587 0 :M FrMacBegin B 0 FmP F FmOP 100.108 452.431 M (m)S FmE 3587 0 :M f148 sf ( )S 3589 0 :M FrMacBegin B 0 FmP F FmOP 105.886 456.431 M ([)S FmE 3590 0 :M f203 sf ( )S 3592 0 :M FrMacBegin B 0 FmP F FmOP 109.213 456.431 M (j)S FmE 3592 0 :M f148 sf ( )S 3594 0 :M FrMacBegin B 0 FmP F FmOP 111.992 456.431 M (] < )S FmE 3595 0 :M f203 sf ( )S 3597 0 :M FrMacBegin B 0 FmP F FmOP 125.959 456.431 M (t)S FmE 3597 0 :M f250 sf ( )S 3599 0 :M FrMacBegin B 0 FmP F FmOP 128.737 452.431 M (j)S FmE 3599 0 :M f148 sf ( )S 3601 0 :M FrMacBegin B 0 FmP F FmOP 76 471.431 M (Otherwise it is queued for later deli)S -0.251 N (v)S -0.151 N (ery)S -0.652 N (.)S 58 483.731 M (2.)S 10.5 N (If the message can be deli)S -0.251 N (v)S -0.151 N (ered to )S FmE 3602 0 :M f203 sf ( )S 3604 0 :M FrMacBegin B 0 FmP F FmOP 214.135 483.731 M (P)S FmE 3604 0 :M f250 sf ( )S 3606 0 :M FrMacBegin B 0 FmP F FmOP 220.243 486.231 M (j)S FmE 3606 0 :M f203 sf ( )S 3608 0 :M FrMacBegin B 0 FmP F FmOP 222.466 483.731 M (, )S FmE 3609 0 :M f148 sf ( )S 3611 0 :M FrMacBegin B 0 FmP F FmOP 227.466 483.731 M (the follo)S -0.251 N (wing three actions occur:)S 76 500.531 M (a.)S 11.062 N (Update all set elements of )S FmE 3611 0 :M f203 sf ( )S 3613 0 :M FrMacBegin B 0 FmP F FmOP 199.991 500.531 M (V)S FmE 3614 0 :M f250 sf ( )S 3616 0 :M FrMacBegin B 0 FmP F FmOP 206.1 503.031 M (j)S FmE 3616 0 :M f148 sf ( )S 3618 0 :M FrMacBegin B 0 FmP F FmOP 208.322 500.531 M ( with the corresponding elements of )S FmE 3618 0 :M f203 sf ( )S 3620 0 :M FrMacBegin B 0 FmP F FmOP 354.03 500.531 M (V)S FmE 3621 0 :M f250 sf ( )S 3623 0 :M FrMacBegin B 0 FmP F FmOP 360.139 496.531 M (m)S FmE 3623 0 :M f148 sf ( )S 3625 0 :M FrMacBegin B 0 FmP F FmOP 365.916 500.531 M (, e)S -0.151 N (xcept for )S FmE 3625 0 :M f203 sf ( )S 3627 0 :M FrMacBegin B 0 FmP F FmOP 413.162 500.531 M (V)S FmE 3628 0 :M f250 sf ( )S 3630 0 :M FrMacBegin B 0 FmP F FmOP 419.271 503.031 M (j)S FmE 3630 0 :M f148 sf ( )S 3632 0 :M FrMacBegin B 0 FmP F FmOP 421.493 500.531 M ([)S FmE 3632 0 :M f203 sf ( )S 3634 0 :M FrMacBegin B 0 FmP F FmOP 424.821 500.531 M (j)S FmE 3635 0 :M f148 sf ( )S 3637 0 :M FrMacBegin B 0 FmP F FmOP 427.599 500.531 M (], as follo)S -0.251 N (ws:)S 94 517.031 M (i.)S 12.722 N (If )S FmE 3637 0 :M f203 sf ( )S 3639 0 :M FrMacBegin B 0 FmP F FmOP 120.804 517.031 M (V)S FmE 3640 0 :M f250 sf ( )S 3642 0 :M FrMacBegin B 0 FmP F FmOP 126.912 519.531 M (j)S FmE 3642 0 :M f148 sf ( )S 3644 0 :M FrMacBegin B 0 FmP F FmOP 129.135 517.031 M ([)S FmE 3644 0 :M f203 sf ( )S 3646 0 :M FrMacBegin B 0 FmP F FmOP 132.462 517.031 M (k)S FmE 3647 0 :M f148 sf ( )S 3649 0 :M FrMacBegin B 0 FmP F FmOP 136.901 517.031 M (] and )S FmE 3649 0 :M f203 sf ( )S 3651 0 :M FrMacBegin B 0 FmP F FmOP 159.315 517.031 M (V)S FmE 3652 0 :M f250 sf ( )S 3654 0 :M FrMacBegin B 0 FmP F FmOP 165.424 513.031 M (m)S FmE 3654 0 :M f148 sf ( )S 3656 0 :M FrMacBegin B 0 FmP F FmOP 171.201 517.031 M ([)S FmE 3656 0 :M f203 sf ( )S 3658 0 :M FrMacBegin B 0 FmP F FmOP 174.529 517.031 M (k)S FmE 3659 0 :M f148 sf ( )S 3661 0 :M FrMacBegin B 0 FmP F FmOP 178.967 517.031 M (] are uninitialized, do nothing.)S 94 533.531 M (ii.)S 9.943 N (If )S FmE 3661 0 :M f203 sf ( )S 3663 0 :M FrMacBegin B 0 FmP F FmOP 120.804 533.531 M (V)S FmE 3664 0 :M f250 sf ( )S 3666 0 :M FrMacBegin B 0 FmP F FmOP 126.912 536.031 M (j)S FmE 3666 0 :M f148 sf ( )S 3668 0 :M FrMacBegin B 0 FmP F FmOP 129.135 533.531 M ([)S FmE 3668 0 :M f203 sf ( )S 3670 0 :M FrMacBegin B 0 FmP F FmOP 132.462 533.531 M (k)S FmE 3671 0 :M f148 sf ( )S 3673 0 :M FrMacBegin B 0 FmP F FmOP 136.901 533.531 M (] is uninitialized and )S FmE 3673 0 :M f203 sf ( )S 3675 0 :M FrMacBegin B 0 FmP F FmOP 220.968 533.531 M (V)S FmE 3676 0 :M f250 sf ( )S 3678 0 :M FrMacBegin B 0 FmP F FmOP 227.077 529.531 M (m)S FmE 3678 0 :M f148 sf ( )S 3680 0 :M FrMacBegin B 0 FmP F FmOP 232.854 533.531 M ([)S FmE 3680 0 :M f203 sf ( )S 3682 0 :M FrMacBegin B 0 FmP F FmOP 236.182 533.531 M (k)S FmE 3683 0 :M f148 sf ( )S 3685 0 :M FrMacBegin B 0 FmP F FmOP 240.62 533.531 M (] is initialized, set )S FmE 3685 0 :M f203 sf ( )S 3687 0 :M FrMacBegin B 0 FmP F FmOP 313.855 533.531 M (V)S FmE 3688 0 :M f250 sf ( )S 3690 0 :M FrMacBegin B 0 FmP F FmOP 319.963 536.031 M (j)S FmE 3690 0 :M f148 sf ( )S 3692 0 :M FrMacBegin B 0 FmP F FmOP 322.186 533.531 M ([)S FmE 3692 0 :M f203 sf ( )S 3694 0 :M FrMacBegin B 0 FmP F FmOP 325.514 533.531 M (k)S FmE 3695 0 :M f148 sf ( )S 3697 0 :M FrMacBegin B 0 FmP F FmOP 329.952 533.531 M (] )S FmE 3697 0 :M f237 sf ( )S 3699 0 :M FrMacBegin B 0 FmP F FmOP 335.78 533.531 M (\254)S FmE 3700 0 :M f148 sf ( )S 3702 0 :M FrMacBegin B 0 FmP F FmOP 345.648 533.531 M ( )S FmE 3702 0 :M f203 sf ( )S 3704 0 :M FrMacBegin B 0 FmP F FmOP 347.796 533.531 M (V)S FmE 3705 0 :M f250 sf ( )S 3707 0 :M FrMacBegin B 0 FmP F FmOP 353.905 529.531 M (m)S FmE 3707 0 :M f148 sf ( )S 3709 0 :M FrMacBegin B 0 FmP F FmOP 359.682 533.531 M ([)S FmE 3709 0 :M f203 sf ( )S 3711 0 :M FrMacBegin B 0 FmP F FmOP 363.01 533.531 M (k)S FmE 3712 0 :M f148 sf ( )S 3714 0 :M FrMacBegin B 0 FmP F FmOP 367.448 533.531 M (].)S 94 550.031 M (iii.)S 7.165 N (If both )S FmE 3714 0 :M f203 sf ( )S 3716 0 :M FrMacBegin B 0 FmP F FmOP 141.082 550.031 M (V)S FmE 3717 0 :M f250 sf ( )S 3719 0 :M FrMacBegin B 0 FmP F FmOP 147.19 552.531 M (j)S FmE 3719 0 :M f148 sf ( )S 3721 0 :M FrMacBegin B 0 FmP F FmOP 149.413 550.031 M ([)S FmE 3721 0 :M f203 sf ( )S 3723 0 :M FrMacBegin B 0 FmP F FmOP 152.741 550.031 M (k)S FmE 3724 0 :M f148 sf ( )S 3726 0 :M FrMacBegin B 0 FmP F FmOP 157.179 550.031 M (] and )S FmE 3726 0 :M f203 sf ( )S 3728 0 :M FrMacBegin B 0 FmP F FmOP 179.594 550.031 M (V)S FmE 3729 0 :M f250 sf ( )S 3731 0 :M FrMacBegin B 0 FmP F FmOP 185.702 546.031 M (m)S FmE 3731 0 :M f148 sf ( )S 3733 0 :M FrMacBegin B 0 FmP F FmOP 191.479 550.031 M ([)S FmE 3733 0 :M f203 sf ( )S 3735 0 :M FrMacBegin B 0 FmP F FmOP 194.807 550.031 M (k)S FmE 3736 0 :M f148 sf ( )S 3738 0 :M FrMacBegin B 0 FmP F FmOP 199.246 550.031 M (] are initialized, )S FmE 3738 0 :M f203 sf ( )S 3740 0 :M FrMacBegin B 0 FmP F FmOP 264.412 550.031 M (V)S FmE 3741 0 :M f250 sf ( )S 3743 0 :M FrMacBegin B 0 FmP F FmOP 270.52 552.531 M (j)S FmE 3743 0 :M f148 sf ( )S 3745 0 :M FrMacBegin B 0 FmP F FmOP 272.743 550.031 M ([)S FmE 3745 0 :M f203 sf ( )S 3747 0 :M FrMacBegin B 0 FmP F FmOP 276.07 550.031 M (k)S FmE 3748 0 :M f148 sf ( )S 3750 0 :M FrMacBegin B 0 FmP F FmOP 280.509 550.031 M (][)S FmE 3750 0 :M f203 sf ( )S 3752 0 :M FrMacBegin B 0 FmP F FmOP 287.164 550.031 M (k)S FmE 3753 0 :M f237 sf ( )S 3755 0 :M FrMacBegin B 0 FmP F FmOP 291.603 550.031 M (\242)S FmE 3755 0 :M f148 sf ( )S 3757 0 :M FrMacBegin B 0 FmP F FmOP 294.073 550.031 M (] )S FmE 3758 0 :M f237 sf ( )S 3760 0 :M FrMacBegin B 0 FmP F FmOP 299.901 550.031 M (\254)S FmE 3760 0 :M f148 sf ( )S 3762 0 :M FrMacBegin B 0 FmP F FmOP 309.769 550.031 M ( max\()S FmE 3763 0 :M f203 sf ( )S 3765 0 :M FrMacBegin B 0 FmP F FmOP 332.813 550.031 M (V)S FmE 3765 0 :M f250 sf ( )S 3767 0 :M FrMacBegin B 0 FmP F FmOP 338.922 552.531 M (j)S FmE 3767 0 :M f148 sf ( )S 3769 0 :M FrMacBegin B 0 FmP F FmOP 341.145 550.031 M ([)S FmE 3770 0 :M f203 sf ( )S 3772 0 :M FrMacBegin B 0 FmP F FmOP 344.472 550.031 M (k)S FmE 3772 0 :M f148 sf ( )S 3774 0 :M FrMacBegin B 0 FmP F FmOP 348.911 550.031 M (][)S FmE 3775 0 :M f203 sf ( )S 3777 0 :M FrMacBegin B 0 FmP F FmOP 355.566 550.031 M (k)S FmE 3777 0 :M f237 sf ( )S 3779 0 :M FrMacBegin B 0 FmP F FmOP 360.004 550.031 M (\242)S FmE 3780 0 :M f148 sf ( )S 3782 0 :M FrMacBegin B 0 FmP F FmOP 362.475 550.031 M (], )S FmE 3782 0 :M f203 sf ( )S 3784 0 :M FrMacBegin B 0 FmP F FmOP 370.451 550.031 M (V)S FmE 3785 0 :M f250 sf ( )S 3787 0 :M FrMacBegin B 0 FmP F FmOP 376.56 546.031 M (m)S FmE 3787 0 :M f148 sf ( )S 3789 0 :M FrMacBegin B 0 FmP F FmOP 382.337 550.031 M ([)S FmE 3789 0 :M f203 sf ( )S 3791 0 :M FrMacBegin B 0 FmP F FmOP 385.665 550.031 M (k)S FmE 3792 0 :M f148 sf ( )S 3794 0 :M FrMacBegin B 0 FmP F FmOP 390.103 550.031 M (][)S FmE 3794 0 :M f203 sf ( )S 3796 0 :M FrMacBegin B 0 FmP F FmOP 396.758 550.031 M (k)S FmE 3797 0 :M f237 sf ( )S 3799 0 :M FrMacBegin B 0 FmP F FmOP 401.197 550.031 M (\242)S FmE 3799 0 :M f148 sf ( )S 3801 0 :M FrMacBegin B 0 FmP F FmOP 403.667 550.031 M (]\) for all )S FmE 3802 0 :M f203 sf ( )S 3804 0 :M FrMacBegin B 0 FmP F FmOP 439.473 550.031 M (k)S FmE 3804 0 :M f237 sf ( )S 3806 0 :M FrMacBegin B 0 FmP F FmOP 443.912 550.031 M (\242)S FmE 3807 0 :M f148 sf ( )S 3809 0 :M FrMacBegin B 0 FmP F FmOP 446.382 550.031 M ( = 1, \311, )S FmE 3809 0 :M f203 sf ( )S 3811 0 :M FrMacBegin B 0 FmP F FmOP 482.022 550.031 M (n)S FmE 3812 0 :M f148 sf ( )S 3814 0 :M FrMacBegin B 0 FmP F FmOP 58 566.83 M (3.)S 10.5 N (Update )S FmE 3814 0 :M f203 sf ( )S 3816 0 :M FrMacBegin B 0 FmP F FmOP 107.375 566.83 M (P)S FmE 3817 0 :M f250 sf ( )S 3819 0 :M FrMacBegin B 0 FmP F FmOP 113.483 569.33 M (j)S FmE 3819 0 :M f148 sf ( )S 3821 0 :M FrMacBegin B 0 FmP F FmOP 115.706 566.83 M (\325)S -0.552 N (s v)S -0.151 N (ector clock for all )S FmE 3821 0 :M f203 sf ( )S 3823 0 :M FrMacBegin B 0 FmP F FmOP 203.008 566.83 M (k)S FmE 3824 0 :M f148 sf ( )S 3826 0 :M FrMacBegin B 0 FmP F FmOP 207.446 566.83 M ( = 1, \311, )S FmE 3826 0 :M f203 sf ( )S 3828 0 :M FrMacBegin B 0 FmP F FmOP 243.086 566.83 M (n)S FmE 3829 0 :M f148 sf ( )S 3831 0 :M FrMacBegin B 0 FmP F FmOP 248.086 566.83 M (: )S FmE 3831 0 :M f203 sf ( )S 3833 0 :M FrMacBegin B 0 FmP F FmOP 253.364 566.83 M (C)S FmE 3834 0 :M f250 sf ( )S 3836 0 :M FrMacBegin B 0 FmP F FmOP 260.034 569.33 M (j)S FmE 3836 0 :M f148 sf ( )S 3838 0 :M FrMacBegin B 0 FmP F FmOP 262.257 566.83 M ([)S FmE 3838 0 :M f203 sf ( )S 3840 0 :M FrMacBegin B 0 FmP F FmOP 265.584 566.83 M (k)S FmE 3841 0 :M f148 sf ( )S 3843 0 :M FrMacBegin B 0 FmP F FmOP 270.023 566.83 M (] )S FmE 3843 0 :M f237 sf ( )S 3845 0 :M FrMacBegin B 0 FmP F FmOP 275.851 566.83 M (\254)S FmE 3846 0 :M f148 sf ( )S 3848 0 :M FrMacBegin B 0 FmP F FmOP 285.719 566.83 M ( max\()S FmE 3848 0 :M f203 sf ( )S 3850 0 :M FrMacBegin B 0 FmP F FmOP 308.763 566.83 M (C)S FmE 3851 0 :M f250 sf ( )S 3853 0 :M FrMacBegin B 0 FmP F FmOP 315.433 569.33 M (j)S FmE 3853 0 :M f148 sf ( )S 3855 0 :M FrMacBegin B 0 FmP F FmOP 317.656 566.83 M ([)S FmE 3855 0 :M f203 sf ( )S 3857 0 :M FrMacBegin B 0 FmP F FmOP 320.983 566.83 M (k)S FmE 3858 0 :M f148 sf ( )S 3860 0 :M FrMacBegin B 0 FmP F FmOP 325.422 566.83 M (], )S FmE 3860 0 :M f203 sf ( )S 3862 0 :M FrMacBegin B 0 FmP F FmOP 333.75 566.83 M (t)S FmE 3863 0 :M f250 sf ( )S 3865 0 :M FrMacBegin B 0 FmP F FmOP 336.528 562.831 M (m)S FmE 3865 0 :M f148 sf ( )S 3867 0 :M FrMacBegin B 0 FmP F FmOP 342.305 566.83 M ([)S FmE 3867 0 :M f203 sf ( )S 3869 0 :M FrMacBegin B 0 FmP F FmOP 345.633 566.83 M (k)S FmE 3870 0 :M f148 sf ( )S 3872 0 :M FrMacBegin B 0 FmP F FmOP 350.071 566.83 M (]\))S 58 580.964 M (4.)S 10.5 N (Check b)S -0.2 N (uf)S -0.251 N (fered messages to see if an)S -0.151 N (y can be deli)S -0.251 N (v)S -0.151 N (ered.)S FmE endp showpage %%PageTrailer %%Page: 7 7 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 7 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 3872 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 3872 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 3872 0 :M f148 sf ( )S 3874 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Schiper-Eggli-Sandoz Protocol)S 61.271 N (ECS 251 \320 Winter 2001)S 159.015 N (Page )S (7)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 3875 0 :M f263 sf ( )S 3878 0 :M FrMacBegin B 0 FmP F FmOP 58 68 M (Example)S FmE 3878 0 :M f148 sf ( )S 3880 0 :M FrMacBegin B 0 FmP F FmOP 58 203 M -0.077(Here is the protocol applied to the abo)W -0.151 N (v)S -0.151 N -0.077(e situation. [ ... ] and { ... } are lik)W -0.1 N -0.077(e \( ... \) b)W -0.2 N -0.077(ut used when too man)W -0.151 N -0.077(y parentheses )W 58 215 M (w)S -0.1 N (ould be confusing \(to me, at an)S -0.151 N (y rate!\):)S FmE 3880 0 :M f203 sf ( )S 3882 0 :M FrMacBegin B 0 FmP F FmOP 58 229.666 M (e)S FmE 3883 0 :M f276 sf ( )S 3885 0 :M FrMacBegin B 0 FmP F FmOP 62.438 232.166 M (31)S FmE 3885 0 :M f148 sf ( )S 3887 0 :M FrMacBegin B 0 FmP F FmOP 70.438 229.666 M (: )S FmE 3887 0 :M f203 sf ( )S 3889 0 :M FrMacBegin B 0 FmP F FmOP 75.717 229.666 M (P)S FmE 3890 0 :M f276 sf ( )S 3892 0 :M FrMacBegin B 0 FmP F FmOP 81.825 232.166 M (3)S FmE 3892 0 :M f148 sf ( )S 3894 0 :M FrMacBegin B 0 FmP F FmOP 85.825 229.666 M ( sends message )S FmE 3894 0 :M f203 sf ( )S 3896 0 :M FrMacBegin B 0 FmP F FmOP 149.414 229.666 M (m)S FmE 3897 0 :M f276 sf ( )S 3899 0 :M FrMacBegin B 0 FmP F FmOP 156.633 232.166 M (3,1)S FmE 3899 0 :M f148 sf ( )S 3901 0 :M FrMacBegin B 0 FmP F FmOP 166.633 229.666 M ( to )S FmE 3901 0 :M f203 sf ( )S 3903 0 :M FrMacBegin B 0 FmP F FmOP 179.412 229.666 M (P)S FmE 3904 0 :M f276 sf ( )S 3906 0 :M FrMacBegin B 0 FmP F FmOP 185.52 232.166 M (2)S FmE 3906 0 :M f148 sf ( )S 3908 0 :M FrMacBegin B 0 FmP F FmOP 189.52 229.666 M (. )S FmE 3908 0 :M f203 sf ( )S 3910 0 :M FrMacBegin B 0 FmP F FmOP 194.52 229.666 M (C)S FmE 3911 0 :M f276 sf ( )S 3913 0 :M FrMacBegin B 0 FmP F FmOP 201.19 232.166 M (3)S FmE 3913 0 :M f148 sf ( )S 3915 0 :M FrMacBegin B 0 FmP F FmOP 205.19 229.666 M ( = \(0, 0, 1\); )S FmE 3915 0 :M f203 sf ( )S 3917 0 :M FrMacBegin B 0 FmP F FmOP 255.263 229.666 M (t)S FmE 3918 0 :M f276 sf ( )S 3920 0 :M FrMacBegin B 0 FmP F FmOP 258.042 225.667 M (3,1)S FmE 3920 0 :M f148 sf ( )S 3922 0 :M FrMacBegin B 0 FmP F FmOP 268.042 229.666 M ( )S FmE 3922 0 :M f237 sf ( )S 3924 0 :M FrMacBegin B 0 FmP F FmOP 270.542 229.666 M (\254)S FmE 3925 0 :M f148 sf ( )S 3927 0 :M FrMacBegin B 0 FmP F FmOP 280.41 229.666 M ( \(0, 0, 1\), )S FmE 3927 0 :M f203 sf ( )S 3929 0 :M FrMacBegin B 0 FmP F FmOP 319.213 229.666 M (V)S FmE 3930 0 :M f276 sf ( )S 3932 0 :M FrMacBegin B 0 FmP F FmOP 325.322 225.667 M (3,1)S FmE 3932 0 :M f148 sf ( )S 3934 0 :M FrMacBegin B 0 FmP F FmOP 335.322 229.666 M ( )S FmE 3934 0 :M f237 sf ( )S 3936 0 :M FrMacBegin B 0 FmP F FmOP 337.822 229.666 M (\254)S FmE 3937 0 :M f148 sf ( )S 3939 0 :M FrMacBegin B 0 FmP F FmOP 347.69 229.666 M ( \(?, ?, ?\); )S FmE 3939 0 :M f203 sf ( )S 3941 0 :M FrMacBegin B 0 FmP F FmOP 385.087 229.666 M (V)S FmE 3942 0 :M f276 sf ( )S 3944 0 :M FrMacBegin B 0 FmP F FmOP 391.196 232.166 M (3)S FmE 3944 0 :M f148 sf ( )S 3946 0 :M FrMacBegin B 0 FmP F FmOP 395.196 229.666 M ( )S FmE 3946 0 :M f237 sf ( )S 3948 0 :M FrMacBegin B 0 FmP F FmOP 397.696 229.666 M (\254)S FmE 3949 0 :M f148 sf ( )S 3951 0 :M FrMacBegin B 0 FmP F FmOP 407.564 229.666 M ( [ ?, \(0, 0, 1\), ? ])S FmE 3951 0 :M f203 sf ( )S 3953 0 :M FrMacBegin B 0 FmP F FmOP 58 246.166 M (e)S FmE 3954 0 :M f276 sf ( )S 3956 0 :M FrMacBegin B 0 FmP F FmOP 62.438 248.666 M (21)S FmE 3956 0 :M f148 sf ( )S 3958 0 :M FrMacBegin B 0 FmP F FmOP 70.438 246.166 M (: )S FmE 3958 0 :M f203 sf ( )S 3960 0 :M FrMacBegin B 0 FmP F FmOP 75.717 246.166 M (P)S FmE 3961 0 :M f276 sf ( )S 3963 0 :M FrMacBegin B 0 FmP F FmOP 81.825 248.666 M (2)S FmE 3963 0 :M f148 sf ( )S 3965 0 :M FrMacBegin B 0 FmP F FmOP 85.825 246.166 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 3965 0 :M f203 sf ( )S 3967 0 :M FrMacBegin B 0 FmP F FmOP 159.543 246.166 M (m)S FmE 3968 0 :M f276 sf ( )S 3970 0 :M FrMacBegin B 0 FmP F FmOP 166.763 248.666 M (3,1)S FmE 3970 0 :M f148 sf ( )S 3972 0 :M FrMacBegin B 0 FmP F FmOP 176.763 246.166 M ( from )S FmE 3972 0 :M f203 sf ( )S 3974 0 :M FrMacBegin B 0 FmP F FmOP 201.196 246.166 M (P)S FmE 3975 0 :M f276 sf ( )S 3977 0 :M FrMacBegin B 0 FmP F FmOP 207.305 248.666 M (3)S FmE 3977 0 :M f148 sf ( )S 3979 0 :M FrMacBegin B 0 FmP F FmOP 211.305 246.166 M (. )S -0.552 N (As )S FmE 3979 0 :M f203 sf ( )S 3981 0 :M FrMacBegin B 0 FmP F FmOP 229.01 246.166 M (V)S FmE 3982 0 :M f276 sf ( )S 3984 0 :M FrMacBegin B 0 FmP F FmOP 235.118 242.166 M (3,1)S FmE 3984 0 :M f148 sf ( )S 3986 0 :M FrMacBegin B 0 FmP F FmOP 245.118 246.166 M ([2] = \(?, ?, ?\)[2] is uninitialized, the message is accepted.)S FmE 3986 0 :M f203 sf ( )S 3988 0 :M FrMacBegin B 0 FmP F FmOP 76 260 M (V)S FmE 3989 0 :M f276 sf ( )S 3991 0 :M FrMacBegin B 0 FmP F FmOP 82.108 262.5 M (2)S FmE 3991 0 :M f148 sf ( )S 3993 0 :M FrMacBegin B 0 FmP F FmOP 86.108 260 M ( )S FmE 3993 0 :M f237 sf ( )S 3995 0 :M FrMacBegin B 0 FmP F FmOP 88.608 260 M (\254)S FmE 3996 0 :M f148 sf ( )S 3998 0 :M FrMacBegin B 0 FmP F FmOP 98.477 260 M ( [ ?, ?, ? ] and)S FmE 3998 0 :M f203 sf ( )S 4000 0 :M FrMacBegin B 0 FmP F FmOP 152.886 260 M ( C)S FmE 4001 0 :M f276 sf ( )S 4003 0 :M FrMacBegin B 0 FmP F FmOP 162.056 262.5 M (2)S FmE 4003 0 :M f148 sf ( )S 4005 0 :M FrMacBegin B 0 FmP F FmOP 166.056 260 M ( )S FmE 4005 0 :M f237 sf ( )S 4007 0 :M FrMacBegin B 0 FmP F FmOP 168.556 260 M (\254)S FmE 4008 0 :M f148 sf ( )S 4010 0 :M FrMacBegin B 0 FmP F FmOP 178.424 260 M ( )S FmE 4010 0 :M f203 sf ( )S 4012 0 :M FrMacBegin B 0 FmP F FmOP 180.924 260 M (max)S FmE 4013 0 :M f148 sf ( )S 4015 0 :M FrMacBegin B 0 FmP F FmOP 197.582 260 M ([\(0, 0, 0\), \(0, 0, 1\)] = \(0, 0, 1\))S FmE 4015 0 :M f203 sf ( )S 4017 0 :M FrMacBegin B 0 FmP F FmOP 58 276.499 M (e)S FmE 4018 0 :M f276 sf ( )S 4020 0 :M FrMacBegin B 0 FmP F FmOP 62.438 278.999 M (22)S FmE 4020 0 :M f148 sf ( )S 4022 0 :M FrMacBegin B 0 FmP F FmOP 70.438 276.499 M (: )S FmE 4022 0 :M f203 sf ( )S 4024 0 :M FrMacBegin B 0 FmP F FmOP 75.717 276.499 M (P)S FmE 4025 0 :M f276 sf ( )S 4027 0 :M FrMacBegin B 0 FmP F FmOP 81.825 278.999 M (2)S FmE 4027 0 :M f148 sf ( )S 4029 0 :M FrMacBegin B 0 FmP F FmOP 85.825 276.499 M ( sends message )S FmE 4029 0 :M f203 sf ( )S 4031 0 :M FrMacBegin B 0 FmP F FmOP 149.414 276.499 M (m)S FmE 4032 0 :M f276 sf ( )S 4034 0 :M FrMacBegin B 0 FmP F FmOP 156.633 278.999 M (2,1)S FmE 4034 0 :M f148 sf ( )S 4036 0 :M FrMacBegin B 0 FmP F FmOP 166.633 276.499 M ( to )S FmE 4036 0 :M f203 sf ( )S 4038 0 :M FrMacBegin B 0 FmP F FmOP 179.412 276.499 M (P)S FmE 4039 0 :M f276 sf ( )S 4041 0 :M FrMacBegin B 0 FmP F FmOP 185.52 278.999 M (1)S FmE 4041 0 :M f148 sf ( )S 4043 0 :M FrMacBegin B 0 FmP F FmOP 189.52 276.499 M (. )S FmE 4043 0 :M f203 sf ( )S 4045 0 :M FrMacBegin B 0 FmP F FmOP 194.52 276.499 M (C)S FmE 4046 0 :M f276 sf ( )S 4048 0 :M FrMacBegin B 0 FmP F FmOP 201.19 278.999 M (2)S FmE 4048 0 :M f148 sf ( )S 4050 0 :M FrMacBegin B 0 FmP F FmOP 205.19 276.499 M ( )S FmE 4050 0 :M f237 sf ( )S 4052 0 :M FrMacBegin B 0 FmP F FmOP 207.69 276.499 M (\254)S FmE 4053 0 :M f148 sf ( )S 4055 0 :M FrMacBegin B 0 FmP F FmOP 217.558 276.499 M ( \(0, 1, 1\); )S FmE 4055 0 :M f203 sf ( )S 4057 0 :M FrMacBegin B 0 FmP F FmOP 256.992 276.499 M (t)S FmE 4058 0 :M f276 sf ( )S 4060 0 :M FrMacBegin B 0 FmP F FmOP 259.77 272.499 M (2,1)S FmE 4060 0 :M f148 sf ( )S 4062 0 :M FrMacBegin B 0 FmP F FmOP 269.77 276.499 M ( )S FmE 4062 0 :M f237 sf ( )S 4064 0 :M FrMacBegin B 0 FmP F FmOP 272.27 276.499 M (\254)S FmE 4065 0 :M f148 sf ( )S 4067 0 :M FrMacBegin B 0 FmP F FmOP 282.138 276.499 M ( \(0, 1, 1\), )S FmE 4067 0 :M f203 sf ( )S 4069 0 :M FrMacBegin B 0 FmP F FmOP 320.942 276.499 M (V)S FmE 4070 0 :M f276 sf ( )S 4072 0 :M FrMacBegin B 0 FmP F FmOP 327.05 272.499 M (2,1)S FmE 4072 0 :M f148 sf ( )S 4074 0 :M FrMacBegin B 0 FmP F FmOP 337.05 276.499 M ( )S FmE 4074 0 :M f237 sf ( )S 4076 0 :M FrMacBegin B 0 FmP F FmOP 339.55 276.499 M (\254)S FmE 4077 0 :M f148 sf ( )S 4079 0 :M FrMacBegin B 0 FmP F FmOP 349.418 276.499 M ( [ ?, ?, ? ]; )S FmE 4079 0 :M f203 sf ( )S 4081 0 :M FrMacBegin B 0 FmP F FmOP 391.816 276.499 M (V)S FmE 4082 0 :M f276 sf ( )S 4084 0 :M FrMacBegin B 0 FmP F FmOP 397.924 278.999 M (2)S FmE 4084 0 :M f148 sf ( )S 4086 0 :M FrMacBegin B 0 FmP F FmOP 401.924 276.499 M ( )S FmE 4086 0 :M f237 sf ( )S 4088 0 :M FrMacBegin B 0 FmP F FmOP 404.424 276.499 M (\254)S FmE 4089 0 :M f148 sf ( )S 4091 0 :M FrMacBegin B 0 FmP F FmOP 414.292 276.499 M ( [ \(0, 1, 1\), ?, ? ])S FmE 4091 0 :M f203 sf ( )S 4093 0 :M FrMacBegin B 0 FmP F FmOP 58 292.999 M (e)S FmE 4094 0 :M f276 sf ( )S 4096 0 :M FrMacBegin B 0 FmP F FmOP 62.438 295.499 M (11)S FmE 4096 0 :M f148 sf ( )S 4098 0 :M FrMacBegin B 0 FmP F FmOP 70.438 292.999 M (: )S FmE 4098 0 :M f203 sf ( )S 4100 0 :M FrMacBegin B 0 FmP F FmOP 75.717 292.999 M (P)S FmE 4101 0 :M f276 sf ( )S 4103 0 :M FrMacBegin B 0 FmP F FmOP 81.825 295.499 M (1)S FmE 4103 0 :M f148 sf ( )S 4105 0 :M FrMacBegin B 0 FmP F FmOP 85.825 292.999 M ( sends message )S FmE 4105 0 :M f203 sf ( )S 4107 0 :M FrMacBegin B 0 FmP F FmOP 149.414 292.999 M (m)S FmE 4108 0 :M f276 sf ( )S 4110 0 :M FrMacBegin B 0 FmP F FmOP 156.633 295.499 M (1,1)S FmE 4110 0 :M f148 sf ( )S 4112 0 :M FrMacBegin B 0 FmP F FmOP 166.633 292.999 M ( to )S FmE 4112 0 :M f203 sf ( )S 4114 0 :M FrMacBegin B 0 FmP F FmOP 179.412 292.999 M (P)S FmE 4115 0 :M f276 sf ( )S 4117 0 :M FrMacBegin B 0 FmP F FmOP 185.52 295.499 M (3)S FmE 4117 0 :M f148 sf ( )S 4119 0 :M FrMacBegin B 0 FmP F FmOP 189.52 292.999 M (. )S FmE 4119 0 :M f203 sf ( )S 4121 0 :M FrMacBegin B 0 FmP F FmOP 194.52 292.999 M (C)S FmE 4122 0 :M f276 sf ( )S 4124 0 :M FrMacBegin B 0 FmP F FmOP 201.19 295.499 M (1)S FmE 4124 0 :M f148 sf ( )S 4126 0 :M FrMacBegin B 0 FmP F FmOP 205.19 292.999 M ( )S FmE 4126 0 :M f237 sf ( )S 4128 0 :M FrMacBegin B 0 FmP F FmOP 207.69 292.999 M (\254)S FmE 4129 0 :M f148 sf ( )S 4131 0 :M FrMacBegin B 0 FmP F FmOP 217.558 292.999 M ( \(1, 0, 0\); )S FmE 4131 0 :M f203 sf ( )S 4133 0 :M FrMacBegin B 0 FmP F FmOP 256.992 292.999 M (t)S FmE 4134 0 :M f276 sf ( )S 4136 0 :M FrMacBegin B 0 FmP F FmOP 259.77 288.999 M (1,1)S FmE 4136 0 :M f148 sf ( )S 4138 0 :M FrMacBegin B 0 FmP F FmOP 269.77 292.999 M ( )S FmE 4138 0 :M f237 sf ( )S 4140 0 :M FrMacBegin B 0 FmP F FmOP 272.27 292.999 M (\254)S FmE 4141 0 :M f148 sf ( )S 4143 0 :M FrMacBegin B 0 FmP F FmOP 282.138 292.999 M ( \(1, 0, 0\), )S FmE 4143 0 :M f203 sf ( )S 4145 0 :M FrMacBegin B 0 FmP F FmOP 320.942 292.999 M (V)S FmE 4146 0 :M f276 sf ( )S 4148 0 :M FrMacBegin B 0 FmP F FmOP 327.05 288.999 M (1,1)S FmE 4148 0 :M f148 sf ( )S 4150 0 :M FrMacBegin B 0 FmP F FmOP 337.05 292.999 M ( )S FmE 4150 0 :M f237 sf ( )S 4152 0 :M FrMacBegin B 0 FmP F FmOP 339.55 292.999 M (\254)S FmE 4153 0 :M f148 sf ( )S 4155 0 :M FrMacBegin B 0 FmP F FmOP 349.418 292.999 M ( \( ?, ?, ? \); )S FmE 4155 0 :M f203 sf ( )S 4157 0 :M FrMacBegin B 0 FmP F FmOP 391.816 292.999 M (V)S FmE 4158 0 :M f276 sf ( )S 4160 0 :M FrMacBegin B 0 FmP F FmOP 397.924 295.499 M (1)S FmE 4160 0 :M f148 sf ( )S 4162 0 :M FrMacBegin B 0 FmP F FmOP 401.924 292.999 M ( )S FmE 4162 0 :M f237 sf ( )S 4164 0 :M FrMacBegin B 0 FmP F FmOP 404.424 292.999 M (\254)S FmE 4165 0 :M f148 sf ( )S 4167 0 :M FrMacBegin B 0 FmP F FmOP 414.292 292.999 M ( [ ?, ?, \(1, 0, 0\) ] )S FmE 4167 0 :M f203 sf ( )S 4169 0 :M FrMacBegin B 0 FmP F FmOP 58 309.499 M (e)S FmE 4170 0 :M f276 sf ( )S 4172 0 :M FrMacBegin B 0 FmP F FmOP 62.438 311.999 M (32)S FmE 4172 0 :M f148 sf ( )S 4174 0 :M FrMacBegin B 0 FmP F FmOP 70.438 309.499 M (: )S FmE 4174 0 :M f203 sf ( )S 4176 0 :M FrMacBegin B 0 FmP F FmOP 75.717 309.499 M (P)S FmE 4177 0 :M f276 sf ( )S 4179 0 :M FrMacBegin B 0 FmP F FmOP 81.825 311.999 M (3)S FmE 4179 0 :M f148 sf ( )S 4181 0 :M FrMacBegin B 0 FmP F FmOP 85.825 309.499 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 4181 0 :M f203 sf ( )S 4183 0 :M FrMacBegin B 0 FmP F FmOP 159.543 309.499 M (m)S FmE 4184 0 :M f276 sf ( )S 4186 0 :M FrMacBegin B 0 FmP F FmOP 166.763 311.999 M (1,1)S FmE 4186 0 :M f148 sf ( )S 4188 0 :M FrMacBegin B 0 FmP F FmOP 176.763 309.499 M ( from )S FmE 4188 0 :M f203 sf ( )S 4190 0 :M FrMacBegin B 0 FmP F FmOP 201.196 309.499 M (P)S FmE 4191 0 :M f276 sf ( )S 4193 0 :M FrMacBegin B 0 FmP F FmOP 207.305 311.999 M (1)S FmE 4193 0 :M f148 sf ( )S 4195 0 :M FrMacBegin B 0 FmP F FmOP 211.305 309.499 M (. )S -0.552 N (As )S FmE 4195 0 :M f203 sf ( )S 4197 0 :M FrMacBegin B 0 FmP F FmOP 229.01 309.499 M (V)S FmE 4198 0 :M f276 sf ( )S 4200 0 :M FrMacBegin B 0 FmP F FmOP 235.118 305.499 M (1,1)S FmE 4200 0 :M f148 sf ( )S 4202 0 :M FrMacBegin B 0 FmP F FmOP 245.118 309.499 M ([3] = \( ?, ?, ? \)[3] is uninitialized, the message is accepted.)S FmE 4202 0 :M f203 sf ( )S 4204 0 :M FrMacBegin B 0 FmP F FmOP 76 323.332 M (V)S FmE 4205 0 :M f276 sf ( )S 4207 0 :M FrMacBegin B 0 FmP F FmOP 82.108 325.832 M (3)S FmE 4207 0 :M f148 sf ( )S 4209 0 :M FrMacBegin B 0 FmP F FmOP 86.108 323.332 M ( )S FmE 4209 0 :M f237 sf ( )S 4211 0 :M FrMacBegin B 0 FmP F FmOP 88.608 323.332 M (\254)S FmE 4212 0 :M f148 sf ( )S 4214 0 :M FrMacBegin B 0 FmP F FmOP 98.477 323.332 M ( [ ?, \(0, 0, 1\), ? ] and )S FmE 4214 0 :M f203 sf ( )S 4216 0 :M FrMacBegin B 0 FmP F FmOP 182.603 323.332 M (C)S FmE 4217 0 :M f276 sf ( )S 4219 0 :M FrMacBegin B 0 FmP F FmOP 189.272 325.832 M (3)S FmE 4219 0 :M f148 sf ( )S 4221 0 :M FrMacBegin B 0 FmP F FmOP 193.272 323.332 M ( )S FmE 4221 0 :M f237 sf ( )S 4223 0 :M FrMacBegin B 0 FmP F FmOP 195.772 323.332 M (\254)S FmE 4224 0 :M f148 sf ( )S 4226 0 :M FrMacBegin B 0 FmP F FmOP 205.641 323.332 M ( )S FmE 4226 0 :M f203 sf ( )S 4228 0 :M FrMacBegin B 0 FmP F FmOP 208.141 323.332 M (max)S FmE 4229 0 :M f148 sf ( )S 4231 0 :M FrMacBegin B 0 FmP F FmOP 224.798 323.332 M ([\(0, 0, 1\), \(1, 0, 0\)] = \(1, 0, 1\).)S FmE 4231 0 :M f203 sf ( )S 4233 0 :M FrMacBegin B 0 FmP F FmOP 58 339.832 M (e)S FmE 4234 0 :M f276 sf ( )S 4236 0 :M FrMacBegin B 0 FmP F FmOP 62.438 342.332 M (12)S FmE 4236 0 :M f148 sf ( )S 4238 0 :M FrMacBegin B 0 FmP F FmOP 70.438 339.832 M (: )S FmE 4238 0 :M f203 sf ( )S 4240 0 :M FrMacBegin B 0 FmP F FmOP 75.717 339.832 M (P)S FmE 4241 0 :M f276 sf ( )S 4243 0 :M FrMacBegin B 0 FmP F FmOP 81.825 342.332 M (1)S FmE 4243 0 :M f148 sf ( )S 4245 0 :M FrMacBegin B 0 FmP F FmOP 85.825 339.832 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 4245 0 :M f203 sf ( )S 4247 0 :M FrMacBegin B 0 FmP F FmOP 159.543 339.832 M (m)S FmE 4248 0 :M f276 sf ( )S 4250 0 :M FrMacBegin B 0 FmP F FmOP 166.763 342.332 M (2,1)S FmE 4250 0 :M f148 sf ( )S 4252 0 :M FrMacBegin B 0 FmP F FmOP 176.763 339.832 M ( from )S FmE 4252 0 :M f203 sf ( )S 4254 0 :M FrMacBegin B 0 FmP F FmOP 201.196 339.832 M (P)S FmE 4255 0 :M f276 sf ( )S 4257 0 :M FrMacBegin B 0 FmP F FmOP 207.305 342.332 M (2)S FmE 4257 0 :M f148 sf ( )S 4259 0 :M FrMacBegin B 0 FmP F FmOP 211.305 339.832 M (. )S -0.552 N (As )S FmE 4259 0 :M f203 sf ( )S 4261 0 :M FrMacBegin B 0 FmP F FmOP 229.01 339.832 M (V)S FmE 4262 0 :M f276 sf ( )S 4264 0 :M FrMacBegin B 0 FmP F FmOP 235.118 335.832 M (2,1)S FmE 4264 0 :M f148 sf ( )S 4266 0 :M FrMacBegin B 0 FmP F FmOP 245.118 339.832 M ([1] = [ ?, ?, ? ][1] is uninitialized, the message is accepted.)S FmE 4266 0 :M f203 sf ( )S 4268 0 :M FrMacBegin B 0 FmP F FmOP 75.333 353.665 M (V)S FmE 4269 0 :M f276 sf ( )S 4271 0 :M FrMacBegin B 0 FmP F FmOP 81.442 356.165 M (1)S FmE 4271 0 :M f148 sf ( )S 4273 0 :M FrMacBegin B 0 FmP F FmOP 85.442 353.665 M ( )S FmE 4273 0 :M f237 sf ( )S 4275 0 :M FrMacBegin B 0 FmP F FmOP 87.942 353.665 M (\254)S FmE 4276 0 :M f148 sf ( )S 4278 0 :M FrMacBegin B 0 FmP F FmOP 97.81 353.665 M ( [ ?, ?, \(1, 0, 0\) ] and )S FmE 4278 0 :M f203 sf ( )S 4280 0 :M FrMacBegin B 0 FmP F FmOP 181.936 353.665 M (C)S FmE 4281 0 :M f276 sf ( )S 4283 0 :M FrMacBegin B 0 FmP F FmOP 188.606 356.165 M (1)S FmE 4283 0 :M f148 sf ( )S 4285 0 :M FrMacBegin B 0 FmP F FmOP 192.606 353.665 M ( )S FmE 4285 0 :M f237 sf ( )S 4287 0 :M FrMacBegin B 0 FmP F FmOP 195.106 353.665 M (\254)S FmE 4288 0 :M f148 sf ( )S 4290 0 :M FrMacBegin B 0 FmP F FmOP 204.974 353.665 M ( )S FmE 4290 0 :M f203 sf ( )S 4292 0 :M FrMacBegin B 0 FmP F FmOP 207.474 353.665 M (max)S FmE 4293 0 :M f148 sf ( )S 4295 0 :M FrMacBegin B 0 FmP F FmOP 224.132 353.665 M ([\(1, 0, 0\), \(0, 1, 1\)] = \(1, 1, 1\))S FmE 4295 0 :M f203 sf ( )S 4297 0 :M FrMacBegin B 0 FmP F FmOP 58 370.165 M (e)S FmE 4298 0 :M f276 sf ( )S 4300 0 :M FrMacBegin B 0 FmP F FmOP 62.438 372.665 M (23)S FmE 4300 0 :M f148 sf ( )S 4302 0 :M FrMacBegin B 0 FmP F FmOP 70.438 370.165 M (: )S FmE 4302 0 :M f203 sf ( )S 4304 0 :M FrMacBegin B 0 FmP F FmOP 75.717 370.165 M (P)S FmE 4305 0 :M f276 sf ( )S 4307 0 :M FrMacBegin B 0 FmP F FmOP 81.825 372.665 M (2)S FmE 4307 0 :M f148 sf ( )S 4309 0 :M FrMacBegin B 0 FmP F FmOP 85.825 370.165 M ( sends message )S FmE 4309 0 :M f203 sf ( )S 4311 0 :M FrMacBegin B 0 FmP F FmOP 149.414 370.165 M (m)S FmE 4312 0 :M f276 sf ( )S 4314 0 :M FrMacBegin B 0 FmP F FmOP 156.633 372.665 M (2,2)S FmE 4314 0 :M f148 sf ( )S 4316 0 :M FrMacBegin B 0 FmP F FmOP 166.633 370.165 M ( to )S FmE 4316 0 :M f203 sf ( )S 4318 0 :M FrMacBegin B 0 FmP F FmOP 179.412 370.165 M (P)S FmE 4319 0 :M f276 sf ( )S 4321 0 :M FrMacBegin B 0 FmP F FmOP 185.52 372.665 M (1)S FmE 4321 0 :M f148 sf ( )S 4323 0 :M FrMacBegin B 0 FmP F FmOP 189.52 370.165 M (. )S FmE 4323 0 :M f203 sf ( )S 4325 0 :M FrMacBegin B 0 FmP F FmOP 194.52 370.165 M (C)S FmE 4326 0 :M f276 sf ( )S 4328 0 :M FrMacBegin B 0 FmP F FmOP 201.19 372.665 M (2)S FmE 4328 0 :M f148 sf ( )S 4330 0 :M FrMacBegin B 0 FmP F FmOP 205.19 370.165 M ( )S FmE 4330 0 :M f237 sf ( )S 4332 0 :M FrMacBegin B 0 FmP F FmOP 207.69 370.165 M (\254)S FmE 4333 0 :M f148 sf ( )S 4335 0 :M FrMacBegin B 0 FmP F FmOP 217.558 370.165 M ( \(0, 2, 1\); )S FmE 4335 0 :M f203 sf ( )S 4337 0 :M FrMacBegin B 0 FmP F FmOP 256.992 370.165 M (t)S FmE 4338 0 :M f276 sf ( )S 4340 0 :M FrMacBegin B 0 FmP F FmOP 259.77 366.165 M (2,2)S FmE 4340 0 :M f148 sf ( )S 4342 0 :M FrMacBegin B 0 FmP F FmOP 269.77 370.165 M ( )S FmE 4342 0 :M f237 sf ( )S 4344 0 :M FrMacBegin B 0 FmP F FmOP 272.27 370.165 M (\254)S FmE 4345 0 :M f148 sf ( )S 4347 0 :M FrMacBegin B 0 FmP F FmOP 282.138 370.165 M ( \(0, 2, 1\), )S FmE 4347 0 :M f203 sf ( )S 4349 0 :M FrMacBegin B 0 FmP F FmOP 320.942 370.165 M (V)S FmE 4350 0 :M f276 sf ( )S 4352 0 :M FrMacBegin B 0 FmP F FmOP 327.05 366.165 M (2,2)S FmE 4352 0 :M f148 sf ( )S 4354 0 :M FrMacBegin B 0 FmP F FmOP 337.05 370.165 M ( )S FmE 4354 0 :M f237 sf ( )S 4356 0 :M FrMacBegin B 0 FmP F FmOP 339.55 370.165 M (\254)S FmE 4357 0 :M f148 sf ( )S 4359 0 :M FrMacBegin B 0 FmP F FmOP 349.418 370.165 M ( [ \(0, 1, 1\), ?, ? ];)S FmE 4359 0 :M f203 sf ( )S 4361 0 :M FrMacBegin B 0 FmP F FmOP 416.884 370.165 M ( )S -0.352 N (V)S FmE 4362 0 :M f276 sf ( )S 4364 0 :M FrMacBegin B 0 FmP F FmOP 425.141 372.665 M (2)S FmE 4364 0 :M f148 sf ( )S 4366 0 :M FrMacBegin B 0 FmP F FmOP 429.141 370.165 M ( )S FmE 4366 0 :M f237 sf ( )S 4368 0 :M FrMacBegin B 0 FmP F FmOP 431.641 370.165 M (\254)S FmE 4369 0 :M f148 sf ( )S 4371 0 :M FrMacBegin B 0 FmP F FmOP 441.509 370.165 M ( [ \(0, 2, 1\), ?, ? ])S FmE 4371 0 :M f203 sf ( )S 4373 0 :M FrMacBegin B 0 FmP F FmOP 58 386.665 M (e)S FmE 4374 0 :M f276 sf ( )S 4376 0 :M FrMacBegin B 0 FmP F FmOP 62.438 389.165 M (13)S FmE 4376 0 :M f148 sf ( )S 4378 0 :M FrMacBegin B 0 FmP F FmOP 70.438 386.665 M (: )S FmE 4378 0 :M f203 sf ( )S 4380 0 :M FrMacBegin B 0 FmP F FmOP 75.717 386.665 M (P)S FmE 4381 0 :M f276 sf ( )S 4383 0 :M FrMacBegin B 0 FmP F FmOP 81.825 389.165 M (1)S FmE 4383 0 :M f148 sf ( )S 4385 0 :M FrMacBegin B 0 FmP F FmOP 85.825 386.665 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 4385 0 :M f203 sf ( )S 4387 0 :M FrMacBegin B 0 FmP F FmOP 159.543 386.665 M (m)S FmE 4388 0 :M f276 sf ( )S 4390 0 :M FrMacBegin B 0 FmP F FmOP 166.763 389.165 M (2,2)S FmE 4390 0 :M f148 sf ( )S 4392 0 :M FrMacBegin B 0 FmP F FmOP 176.763 386.665 M ( from )S FmE 4392 0 :M f203 sf ( )S 4394 0 :M FrMacBegin B 0 FmP F FmOP 201.196 386.665 M (P)S FmE 4395 0 :M f276 sf ( )S 4397 0 :M FrMacBegin B 0 FmP F FmOP 207.305 389.165 M (2)S FmE 4397 0 :M f148 sf ( )S 4399 0 :M FrMacBegin B 0 FmP F FmOP 211.305 386.665 M (. )S FmE 4399 0 :M f203 sf ( )S 4401 0 :M FrMacBegin B 0 FmP F FmOP 216.124 386.665 M (As)S FmE 4402 0 :M f148 sf ( )S 4404 0 :M FrMacBegin B 0 FmP F FmOP 226.122 386.665 M ( )S FmE 4404 0 :M f203 sf ( )S 4406 0 :M FrMacBegin B 0 FmP F FmOP 228.27 386.665 M (V)S FmE 4407 0 :M f276 sf ( )S 4409 0 :M FrMacBegin B 0 FmP F FmOP 234.378 382.665 M (2,2)S FmE 4409 0 :M f148 sf ( )S 4411 0 :M FrMacBegin B 0 FmP F FmOP 244.378 386.665 M ([1] = \(0, 1, 1\) < \(1, 1, 1\) = )S FmE 4411 0 :M f203 sf ( )S 4413 0 :M FrMacBegin B 0 FmP F FmOP 353.763 386.665 M (C)S FmE 4414 0 :M f276 sf ( )S 4416 0 :M FrMacBegin B 0 FmP F FmOP 360.433 389.165 M (1)S FmE 4416 0 :M f148 sf ( )S 4418 0 :M FrMacBegin B 0 FmP F FmOP 364.433 386.665 M (, the message is accepted.)S FmE 4418 0 :M f203 sf ( )S 4420 0 :M FrMacBegin B 0 FmP F FmOP 75.333 400.498 M (V)S FmE 4421 0 :M f276 sf ( )S 4423 0 :M FrMacBegin B 0 FmP F FmOP 81.442 402.998 M (1)S FmE 4423 0 :M f148 sf ( )S 4425 0 :M FrMacBegin B 0 FmP F FmOP 85.442 400.498 M ( )S FmE 4425 0 :M f237 sf ( )S 4427 0 :M FrMacBegin B 0 FmP F FmOP 87.942 400.498 M (\254)S FmE 4428 0 :M f148 sf ( )S 4430 0 :M FrMacBegin B 0 FmP F FmOP 97.81 400.498 M ( [ ?, ?, \(1, 0, 0\) ] and )S FmE 4430 0 :M f203 sf ( )S 4432 0 :M FrMacBegin B 0 FmP F FmOP 181.936 400.498 M (C)S FmE 4433 0 :M f276 sf ( )S 4435 0 :M FrMacBegin B 0 FmP F FmOP 188.606 402.998 M (1)S FmE 4435 0 :M f148 sf ( )S 4437 0 :M FrMacBegin B 0 FmP F FmOP 192.606 400.498 M ( )S FmE 4437 0 :M f237 sf ( )S 4439 0 :M FrMacBegin B 0 FmP F FmOP 195.106 400.498 M (\254)S FmE 4440 0 :M f148 sf ( )S 4442 0 :M FrMacBegin B 0 FmP F FmOP 204.974 400.498 M ( )S FmE 4442 0 :M f203 sf ( )S 4444 0 :M FrMacBegin B 0 FmP F FmOP 207.474 400.498 M (max)S FmE 4445 0 :M f148 sf ( )S 4447 0 :M FrMacBegin B 0 FmP F FmOP 224.132 400.498 M ([\(0, 2, 1\), \(1, 1, 1\)] = \(1, 2, 1\))S FmE 58 72 468 118 rC 4447 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP 112 90.804 FmB 378 0 FmL 2 1 FmSo 111.333 126.804 FmB 378 0 FmL 2 1 FmSo 112 171.804 FmB 378 0 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 259.5 90.971 FmAF T 0 360 4.5 4.5 0 259.5 90.971 2 1 F FmAP 0 360 4.5 4.5 0 T 200.833 126.971 FmAF T 0 360 4.5 4.5 0 200.833 126.971 2 1 F FmAP 0 360 4.5 4.5 0 T 251.5 126.971 FmAF T 0 360 4.5 4.5 0 251.5 126.971 2 1 F FmAP 0 360 4.5 4.5 0 T 163.5 172.971 FmAF T 0 360 4.5 4.5 0 163.5 172.971 2 1 F FmAP 0 360 4.167 4.5 0 T 342.5 172.356 FmAF T 0 360 4.167 4.5 0 342.5 172.356 2 1 F FmAP 0 360 4.5 4.5 0 T 390.833 90.971 FmAF T 0 360 4.5 4.5 0 390.833 90.971 2 1 F FmAP FmE 4447 0 :M f289 sf ( )S 4450 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP 91.333 91.171 M (P)S FmE 4450 0 :M f148 sf ( )S 4452 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 94.171 M 0.96 0.96 scale (1)S FmR FmE 4453 0 :M f289 sf ( )S 4456 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP 91.333 128.505 M (P)S FmE 4456 0 :M f148 sf ( )S 4458 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 131.505 M 0.96 0.96 scale (2)S FmR FmE 4458 0 :M f289 sf ( )S 4461 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP 91.333 175.171 M (P)S FmE 4461 0 :M f148 sf ( )S 4463 0 :M FrMacBegin 58 72 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 178.171 M 0.96 0.96 scale (3)S FmR FmG 258.126 80.917 M 0.96 0.96 scale (e11)S FmR FmG 198.667 119.504 M 0.96 0.96 scale (e21)S FmR FmG 252 119.504 M 0.96 0.96 scale (e22)S FmR FmG 147.333 164.171 M 0.96 0.96 scale (e31)S FmR FmG 340.667 164.89 M 0.96 0.96 scale (e32)S FmR FmG 384.667 83.505 M 0.96 0.96 scale (e12)S FmR 375.815 95.979 FmB -0.826 -3.371 FmL 12.583 0.491 FmL -10.931 6.252 FmL 1 FmS 375.815 95.979 FmB -0.826 -3.371 FmL 12.583 0.491 FmL -10.931 6.252 FmL FmFl 256.667 125.171 FmB 118.662 -29.073 FmL 2 1 FmSo 329.842 159.153 FmB 2.373 -2.533 FmL 6.463 10.808 FmL -11.208 -5.741 FmL 1 FmS 329.842 159.153 FmB 2.373 -2.533 FmL 6.463 10.808 FmL -11.208 -5.741 FmL FmFl 256 90 FmB 73.477 68.812 FmL 2 1 FmSo 190.319 140.443 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL 1 FmS 190.319 140.443 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL FmFl 165.333 169.838 FmB 24.662 -29.014 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 398.167 126.971 FmAF T 0 360 4.5 4.5 0 398.167 126.971 2 1 F FmAP FmG 404.667 135.505 M 0.96 0.96 scale (e23)S FmR 450.961 97.707 FmB -1.589 -3.086 FmL 12.35 -2.458 FmL -9.171 8.629 FmL 1 FmS 450.961 97.707 FmB -1.589 -3.086 FmL 12.35 -2.458 FmL -9.171 8.629 FmL FmFl 397.333 125.333 FmB 53.183 -27.397 FmL 2 1 FmSo FmG 464 84.838 M 0.96 0.96 scale (e13)S FmR 0 360 4.5 4.5 0 T 466.833 90.304 FmAF T 0 360 4.5 4.5 0 466.833 90.304 2 1 F FmAP FmE endp showpage %%PageTrailer %%Page: 8 8 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 8 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 4464 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 4464 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 4464 0 :M f148 sf ( )S 4466 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Schiper-Eggli-Sandoz Protocol)S 61.271 N (ECS 251 \320 Winter 2001)S 159.015 N (Page )S (8)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S 58 68 M (No)S -0.251 N (w)S -0.652 N (, suppose )S FmE 4467 0 :M f203 sf ( )S 4469 0 :M FrMacBegin B 0 FmP F FmOP 116.252 68 M (m)S FmE 4469 0 :M f276 sf ( )S 4471 0 :M FrMacBegin B 0 FmP F FmOP 123.471 70.5 M (2,1)S FmE 4471 0 :M f148 sf ( )S 4473 0 :M FrMacBegin B 0 FmP F FmOP 133.471 68 M ( arri)S -0.251 N (v)S -0.151 N (ed as e)S -0.251 N (v)S -0.151 N (ent )S FmE 4474 0 :M f203 sf ( )S 4476 0 :M FrMacBegin B 0 FmP F FmOP 200.959 68 M (e)S FmE 4476 0 :M f276 sf ( )S 4478 0 :M FrMacBegin B 0 FmP F FmOP 205.397 70.5 M (13)S FmE 4478 0 :M f148 sf ( )S 4480 0 :M FrMacBegin B 0 FmP F FmOP 213.397 68 M (, and )S FmE 4481 0 :M f203 sf ( )S 4483 0 :M FrMacBegin B 0 FmP F FmOP 235.336 68 M (m)S FmE 4483 0 :M f276 sf ( )S 4485 0 :M FrMacBegin B 0 FmP F FmOP 242.555 70.5 M (2,2)S FmE 4485 0 :M f148 sf ( )S 4487 0 :M FrMacBegin B 0 FmP F FmOP 252.555 68 M ( as e)S -0.251 N (v)S -0.151 N (ent )S FmE 4488 0 :M f203 sf ( )S 4490 0 :M FrMacBegin B 0 FmP F FmOP 289.635 68 M (e)S FmE 4490 0 :M f276 sf ( )S 4492 0 :M FrMacBegin B 0 FmP F FmOP 294.074 70.5 M (12)S FmE 4492 0 :M f148 sf ( )S 4494 0 :M FrMacBegin B 0 FmP F FmOP 302.074 68 M (:)S FmE 4495 0 :M f203 sf ( )S 4497 0 :M FrMacBegin B 0 FmP F FmOP 58 206.833 M (e)S FmE 4497 0 :M f276 sf ( )S 4499 0 :M FrMacBegin B 0 FmP F FmOP 62.438 209.333 M (31)S FmE 4499 0 :M f148 sf ( )S 4501 0 :M FrMacBegin B 0 FmP F FmOP 70.438 206.833 M (: )S FmE 4502 0 :M f203 sf ( )S 4504 0 :M FrMacBegin B 0 FmP F FmOP 75.717 206.833 M (P)S FmE 4504 0 :M f276 sf ( )S 4506 0 :M FrMacBegin B 0 FmP F FmOP 81.825 209.333 M (3)S FmE 4506 0 :M f148 sf ( )S 4508 0 :M FrMacBegin B 0 FmP F FmOP 85.825 206.833 M ( sends message )S FmE 4509 0 :M f203 sf ( )S 4511 0 :M FrMacBegin B 0 FmP F FmOP 149.414 206.833 M (m)S FmE 4511 0 :M f276 sf ( )S 4513 0 :M FrMacBegin B 0 FmP F FmOP 156.633 209.333 M (3,1)S FmE 4513 0 :M f148 sf ( )S 4515 0 :M FrMacBegin B 0 FmP F FmOP 166.633 206.833 M ( to )S FmE 4516 0 :M f203 sf ( )S 4518 0 :M FrMacBegin B 0 FmP F FmOP 179.412 206.833 M (P)S FmE 4518 0 :M f276 sf ( )S 4520 0 :M FrMacBegin B 0 FmP F FmOP 185.52 209.333 M (2)S FmE 4520 0 :M f148 sf ( )S 4522 0 :M FrMacBegin B 0 FmP F FmOP 189.52 206.833 M (. )S FmE 4523 0 :M f203 sf ( )S 4525 0 :M FrMacBegin B 0 FmP F FmOP 194.52 206.833 M (C)S FmE 4525 0 :M f276 sf ( )S 4527 0 :M FrMacBegin B 0 FmP F FmOP 201.19 209.333 M (3)S FmE 4527 0 :M f148 sf ( )S 4529 0 :M FrMacBegin B 0 FmP F FmOP 205.19 206.833 M ( = \(0, 0, 1\); )S FmE 4530 0 :M f203 sf ( )S 4532 0 :M FrMacBegin B 0 FmP F FmOP 255.263 206.833 M (t)S FmE 4532 0 :M f276 sf ( )S 4534 0 :M FrMacBegin B 0 FmP F FmOP 258.042 202.833 M (3,1)S FmE 4534 0 :M f148 sf ( )S 4536 0 :M FrMacBegin B 0 FmP F FmOP 268.042 206.833 M ( )S FmE 4537 0 :M f237 sf ( )S 4539 0 :M FrMacBegin B 0 FmP F FmOP 270.542 206.833 M (\254)S FmE 4539 0 :M f148 sf ( )S 4541 0 :M FrMacBegin B 0 FmP F FmOP 280.41 206.833 M ( \(0, 0, 1\), )S FmE 4542 0 :M f203 sf ( )S 4544 0 :M FrMacBegin B 0 FmP F FmOP 319.213 206.833 M (V)S FmE 4544 0 :M f276 sf ( )S 4546 0 :M FrMacBegin B 0 FmP F FmOP 325.322 202.833 M (3,1)S FmE 4546 0 :M f148 sf ( )S 4548 0 :M FrMacBegin B 0 FmP F FmOP 335.322 206.833 M ( )S FmE 4549 0 :M f237 sf ( )S 4551 0 :M FrMacBegin B 0 FmP F FmOP 337.822 206.833 M (\254)S FmE 4551 0 :M f148 sf ( )S 4553 0 :M FrMacBegin B 0 FmP F FmOP 347.69 206.833 M ( \(?, ?, ?\); )S FmE 4554 0 :M f203 sf ( )S 4556 0 :M FrMacBegin B 0 FmP F FmOP 385.087 206.833 M (V)S FmE 4556 0 :M f276 sf ( )S 4558 0 :M FrMacBegin B 0 FmP F FmOP 391.196 209.333 M (3)S FmE 4558 0 :M f148 sf ( )S 4560 0 :M FrMacBegin B 0 FmP F FmOP 395.196 206.833 M ( )S FmE 4561 0 :M f237 sf ( )S 4563 0 :M FrMacBegin B 0 FmP F FmOP 397.696 206.833 M (\254)S FmE 4563 0 :M f148 sf ( )S 4565 0 :M FrMacBegin B 0 FmP F FmOP 407.564 206.833 M ( [ ?, \(0, 0, 1\), ? ])S FmE 4566 0 :M f203 sf ( )S 4568 0 :M FrMacBegin B 0 FmP F FmOP 58 223.333 M (e)S FmE 4568 0 :M f276 sf ( )S 4570 0 :M FrMacBegin B 0 FmP F FmOP 62.438 225.833 M (21)S FmE 4570 0 :M f148 sf ( )S 4572 0 :M FrMacBegin B 0 FmP F FmOP 70.438 223.333 M (: )S FmE 4573 0 :M f203 sf ( )S 4575 0 :M FrMacBegin B 0 FmP F FmOP 75.717 223.333 M (P)S FmE 4575 0 :M f276 sf ( )S 4577 0 :M FrMacBegin B 0 FmP F FmOP 81.825 225.833 M (2)S FmE 4577 0 :M f148 sf ( )S 4579 0 :M FrMacBegin B 0 FmP F FmOP 85.825 223.333 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 4580 0 :M f203 sf ( )S 4582 0 :M FrMacBegin B 0 FmP F FmOP 159.543 223.333 M (m)S FmE 4582 0 :M f276 sf ( )S 4584 0 :M FrMacBegin B 0 FmP F FmOP 166.763 225.833 M (3,1)S FmE 4584 0 :M f148 sf ( )S 4586 0 :M FrMacBegin B 0 FmP F FmOP 176.763 223.333 M ( from )S FmE 4587 0 :M f203 sf ( )S 4589 0 :M FrMacBegin B 0 FmP F FmOP 201.196 223.333 M (P)S FmE 4589 0 :M f276 sf ( )S 4591 0 :M FrMacBegin B 0 FmP F FmOP 207.305 225.833 M (3)S FmE 4591 0 :M f148 sf ( )S 4593 0 :M FrMacBegin B 0 FmP F FmOP 211.305 223.333 M (. )S -0.552 N (As )S FmE 4594 0 :M f203 sf ( )S 4596 0 :M FrMacBegin B 0 FmP F FmOP 229.01 223.333 M (V)S FmE 4596 0 :M f276 sf ( )S 4598 0 :M FrMacBegin B 0 FmP F FmOP 235.118 219.333 M (3,1)S FmE 4598 0 :M f148 sf ( )S 4600 0 :M FrMacBegin B 0 FmP F FmOP 245.118 223.333 M ([2] = \(?, ?, ?\)[2] is uninitialized, the message is accepted.)S FmE 4601 0 :M f203 sf ( )S 4603 0 :M FrMacBegin B 0 FmP F FmOP 76 237.166 M (V)S FmE 4603 0 :M f276 sf ( )S 4605 0 :M FrMacBegin B 0 FmP F FmOP 82.108 239.666 M (2)S FmE 4605 0 :M f148 sf ( )S 4607 0 :M FrMacBegin B 0 FmP F FmOP 86.108 237.166 M ( )S FmE 4608 0 :M f237 sf ( )S 4610 0 :M FrMacBegin B 0 FmP F FmOP 88.608 237.166 M (\254)S FmE 4610 0 :M f148 sf ( )S 4612 0 :M FrMacBegin B 0 FmP F FmOP 98.477 237.166 M ( [ ?, ?, ? ] and)S FmE 4613 0 :M f203 sf ( )S 4615 0 :M FrMacBegin B 0 FmP F FmOP 152.886 237.166 M ( C)S FmE 4615 0 :M f276 sf ( )S 4617 0 :M FrMacBegin B 0 FmP F FmOP 162.056 239.666 M (2)S FmE 4617 0 :M f148 sf ( )S 4619 0 :M FrMacBegin B 0 FmP F FmOP 166.056 237.166 M ( )S FmE 4620 0 :M f237 sf ( )S 4622 0 :M FrMacBegin B 0 FmP F FmOP 168.556 237.166 M (\254)S FmE 4622 0 :M f148 sf ( )S 4624 0 :M FrMacBegin B 0 FmP F FmOP 178.424 237.166 M ( )S FmE 4625 0 :M f203 sf ( )S 4627 0 :M FrMacBegin B 0 FmP F FmOP 180.924 237.166 M (max)S FmE 4627 0 :M f148 sf ( )S 4629 0 :M FrMacBegin B 0 FmP F FmOP 197.582 237.166 M ([\(0, 0, 0\), \(0, 0, 1\)] = \(0, 0, 1\))S FmE 4630 0 :M f203 sf ( )S 4632 0 :M FrMacBegin B 0 FmP F FmOP 58 253.666 M (e)S FmE 4632 0 :M f276 sf ( )S 4634 0 :M FrMacBegin B 0 FmP F FmOP 62.438 256.166 M (22)S FmE 4634 0 :M f148 sf ( )S 4636 0 :M FrMacBegin B 0 FmP F FmOP 70.438 253.666 M (: )S FmE 4637 0 :M f203 sf ( )S 4639 0 :M FrMacBegin B 0 FmP F FmOP 75.717 253.666 M (P)S FmE 4639 0 :M f276 sf ( )S 4641 0 :M FrMacBegin B 0 FmP F FmOP 81.825 256.166 M (2)S FmE 4641 0 :M f148 sf ( )S 4643 0 :M FrMacBegin B 0 FmP F FmOP 85.825 253.666 M ( sends message )S FmE 4644 0 :M f203 sf ( )S 4646 0 :M FrMacBegin B 0 FmP F FmOP 149.414 253.666 M (m)S FmE 4646 0 :M f276 sf ( )S 4648 0 :M FrMacBegin B 0 FmP F FmOP 156.633 256.166 M (2,1)S FmE 4648 0 :M f148 sf ( )S 4650 0 :M FrMacBegin B 0 FmP F FmOP 166.633 253.666 M ( to )S FmE 4651 0 :M f203 sf ( )S 4653 0 :M FrMacBegin B 0 FmP F FmOP 179.412 253.666 M (P)S FmE 4653 0 :M f276 sf ( )S 4655 0 :M FrMacBegin B 0 FmP F FmOP 185.52 256.166 M (1)S FmE 4655 0 :M f148 sf ( )S 4657 0 :M FrMacBegin B 0 FmP F FmOP 189.52 253.666 M (. )S FmE 4658 0 :M f203 sf ( )S 4660 0 :M FrMacBegin B 0 FmP F FmOP 194.52 253.666 M (C)S FmE 4660 0 :M f276 sf ( )S 4662 0 :M FrMacBegin B 0 FmP F FmOP 201.19 256.166 M (2)S FmE 4662 0 :M f148 sf ( )S 4664 0 :M FrMacBegin B 0 FmP F FmOP 205.19 253.666 M ( )S FmE 4665 0 :M f237 sf ( )S 4667 0 :M FrMacBegin B 0 FmP F FmOP 207.69 253.666 M (\254)S FmE 4667 0 :M f148 sf ( )S 4669 0 :M FrMacBegin B 0 FmP F FmOP 217.558 253.666 M ( \(0, 1, 1\); )S FmE 4670 0 :M f203 sf ( )S 4672 0 :M FrMacBegin B 0 FmP F FmOP 256.992 253.666 M (t)S FmE 4672 0 :M f276 sf ( )S 4674 0 :M FrMacBegin B 0 FmP F FmOP 259.77 249.666 M (2,1)S FmE 4674 0 :M f148 sf ( )S 4676 0 :M FrMacBegin B 0 FmP F FmOP 269.77 253.666 M ( )S FmE 4677 0 :M f237 sf ( )S 4679 0 :M FrMacBegin B 0 FmP F FmOP 272.27 253.666 M (\254)S FmE 4679 0 :M f148 sf ( )S 4681 0 :M FrMacBegin B 0 FmP F FmOP 282.138 253.666 M ( \(0, 1, 1\), )S FmE 4682 0 :M f203 sf ( )S 4684 0 :M FrMacBegin B 0 FmP F FmOP 320.942 253.666 M (V)S FmE 4684 0 :M f276 sf ( )S 4686 0 :M FrMacBegin B 0 FmP F FmOP 327.05 249.666 M (2,1)S FmE 4686 0 :M f148 sf ( )S 4688 0 :M FrMacBegin B 0 FmP F FmOP 337.05 253.666 M ( )S FmE 4689 0 :M f237 sf ( )S 4691 0 :M FrMacBegin B 0 FmP F FmOP 339.55 253.666 M (\254)S FmE 4691 0 :M f148 sf ( )S 4693 0 :M FrMacBegin B 0 FmP F FmOP 349.418 253.666 M ( [ ?, ?, ? ]; )S FmE 4694 0 :M f203 sf ( )S 4696 0 :M FrMacBegin B 0 FmP F FmOP 391.816 253.666 M (V)S FmE 4696 0 :M f276 sf ( )S 4698 0 :M FrMacBegin B 0 FmP F FmOP 397.924 256.166 M (2)S FmE 4698 0 :M f148 sf ( )S 4700 0 :M FrMacBegin B 0 FmP F FmOP 401.924 253.666 M ( )S FmE 4701 0 :M f237 sf ( )S 4703 0 :M FrMacBegin B 0 FmP F FmOP 404.424 253.666 M (\254)S FmE 4703 0 :M f148 sf ( )S 4705 0 :M FrMacBegin B 0 FmP F FmOP 414.292 253.666 M ( [ \(0, 1, 1\), ?, ? ])S FmE 4706 0 :M f203 sf ( )S 4708 0 :M FrMacBegin B 0 FmP F FmOP 58 270.166 M (e)S FmE 4708 0 :M f276 sf ( )S 4710 0 :M FrMacBegin B 0 FmP F FmOP 62.438 272.666 M (11)S FmE 4710 0 :M f148 sf ( )S 4712 0 :M FrMacBegin B 0 FmP F FmOP 70.438 270.166 M (: )S FmE 4713 0 :M f203 sf ( )S 4715 0 :M FrMacBegin B 0 FmP F FmOP 75.717 270.166 M (P)S FmE 4715 0 :M f276 sf ( )S 4717 0 :M FrMacBegin B 0 FmP F FmOP 81.825 272.666 M (1)S FmE 4717 0 :M f148 sf ( )S 4719 0 :M FrMacBegin B 0 FmP F FmOP 85.825 270.166 M ( sends message )S FmE 4720 0 :M f203 sf ( )S 4722 0 :M FrMacBegin B 0 FmP F FmOP 149.414 270.166 M (m)S FmE 4722 0 :M f276 sf ( )S 4724 0 :M FrMacBegin B 0 FmP F FmOP 156.633 272.666 M (1,1)S FmE 4724 0 :M f148 sf ( )S 4726 0 :M FrMacBegin B 0 FmP F FmOP 166.633 270.166 M ( to )S FmE 4727 0 :M f203 sf ( )S 4729 0 :M FrMacBegin B 0 FmP F FmOP 179.412 270.166 M (P)S FmE 4729 0 :M f276 sf ( )S 4731 0 :M FrMacBegin B 0 FmP F FmOP 185.52 272.666 M (3)S FmE 4731 0 :M f148 sf ( )S 4733 0 :M FrMacBegin B 0 FmP F FmOP 189.52 270.166 M (. )S FmE 4734 0 :M f203 sf ( )S 4736 0 :M FrMacBegin B 0 FmP F FmOP 194.52 270.166 M (C)S FmE 4736 0 :M f276 sf ( )S 4738 0 :M FrMacBegin B 0 FmP F FmOP 201.19 272.666 M (1)S FmE 4738 0 :M f148 sf ( )S 4740 0 :M FrMacBegin B 0 FmP F FmOP 205.19 270.166 M ( )S FmE 4741 0 :M f237 sf ( )S 4743 0 :M FrMacBegin B 0 FmP F FmOP 207.69 270.166 M (\254)S FmE 4743 0 :M f148 sf ( )S 4745 0 :M FrMacBegin B 0 FmP F FmOP 217.558 270.166 M ( \(1, 0, 0\); )S FmE 4746 0 :M f203 sf ( )S 4748 0 :M FrMacBegin B 0 FmP F FmOP 256.992 270.166 M (t)S FmE 4748 0 :M f276 sf ( )S 4750 0 :M FrMacBegin B 0 FmP F FmOP 259.77 266.166 M (1,1)S FmE 4750 0 :M f148 sf ( )S 4752 0 :M FrMacBegin B 0 FmP F FmOP 269.77 270.166 M ( )S FmE 4753 0 :M f237 sf ( )S 4755 0 :M FrMacBegin B 0 FmP F FmOP 272.27 270.166 M (\254)S FmE 4755 0 :M f148 sf ( )S 4757 0 :M FrMacBegin B 0 FmP F FmOP 282.138 270.166 M ( \(1, 0, 0\), )S FmE 4758 0 :M f203 sf ( )S 4760 0 :M FrMacBegin B 0 FmP F FmOP 320.942 270.166 M (V)S FmE 4760 0 :M f276 sf ( )S 4762 0 :M FrMacBegin B 0 FmP F FmOP 327.05 266.166 M (1,1)S FmE 4762 0 :M f148 sf ( )S 4764 0 :M FrMacBegin B 0 FmP F FmOP 337.05 270.166 M ( )S FmE 4765 0 :M f237 sf ( )S 4767 0 :M FrMacBegin B 0 FmP F FmOP 339.55 270.166 M (\254)S FmE 4767 0 :M f148 sf ( )S 4769 0 :M FrMacBegin B 0 FmP F FmOP 349.418 270.166 M ( \( ?, ?, ? \); )S FmE 4770 0 :M f203 sf ( )S 4772 0 :M FrMacBegin B 0 FmP F FmOP 391.816 270.166 M (V)S FmE 4772 0 :M f276 sf ( )S 4774 0 :M FrMacBegin B 0 FmP F FmOP 397.924 272.666 M (1)S FmE 4774 0 :M f148 sf ( )S 4776 0 :M FrMacBegin B 0 FmP F FmOP 401.924 270.166 M ( )S FmE 4777 0 :M f237 sf ( )S 4779 0 :M FrMacBegin B 0 FmP F FmOP 404.424 270.166 M (\254)S FmE 4779 0 :M f148 sf ( )S 4781 0 :M FrMacBegin B 0 FmP F FmOP 414.292 270.166 M ( [ ?, ?, \(1, 0, 0\) ] )S FmE 4782 0 :M f203 sf ( )S 4784 0 :M FrMacBegin B 0 FmP F FmOP 58 286.666 M (e)S FmE 4784 0 :M f276 sf ( )S 4786 0 :M FrMacBegin B 0 FmP F FmOP 62.438 289.166 M (32)S FmE 4786 0 :M f148 sf ( )S 4788 0 :M FrMacBegin B 0 FmP F FmOP 70.438 286.666 M (: )S FmE 4789 0 :M f203 sf ( )S 4791 0 :M FrMacBegin B 0 FmP F FmOP 75.717 286.666 M (P)S FmE 4791 0 :M f276 sf ( )S 4793 0 :M FrMacBegin B 0 FmP F FmOP 81.825 289.166 M (3)S FmE 4793 0 :M f148 sf ( )S 4795 0 :M FrMacBegin B 0 FmP F FmOP 85.825 286.666 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 4796 0 :M f203 sf ( )S 4798 0 :M FrMacBegin B 0 FmP F FmOP 159.543 286.666 M (m)S FmE 4798 0 :M f276 sf ( )S 4800 0 :M FrMacBegin B 0 FmP F FmOP 166.763 289.166 M (1,1)S FmE 4800 0 :M f148 sf ( )S 4802 0 :M FrMacBegin B 0 FmP F FmOP 176.763 286.666 M ( from )S FmE 4803 0 :M f203 sf ( )S 4805 0 :M FrMacBegin B 0 FmP F FmOP 201.196 286.666 M (P)S FmE 4805 0 :M f276 sf ( )S 4807 0 :M FrMacBegin B 0 FmP F FmOP 207.305 289.166 M (1)S FmE 4807 0 :M f148 sf ( )S 4809 0 :M FrMacBegin B 0 FmP F FmOP 211.305 286.666 M (. )S -0.552 N (As )S FmE 4810 0 :M f203 sf ( )S 4812 0 :M FrMacBegin B 0 FmP F FmOP 229.01 286.666 M (V)S FmE 4812 0 :M f276 sf ( )S 4814 0 :M FrMacBegin B 0 FmP F FmOP 235.118 282.666 M (1,1)S FmE 4814 0 :M f148 sf ( )S 4816 0 :M FrMacBegin B 0 FmP F FmOP 245.118 286.666 M ([3] = \( ?, ?, ? \)[3] is uninitialized, the message is accepted.)S FmE 4817 0 :M f203 sf ( )S 4819 0 :M FrMacBegin B 0 FmP F FmOP 76 300.499 M (V)S FmE 4819 0 :M f276 sf ( )S 4821 0 :M FrMacBegin B 0 FmP F FmOP 82.108 302.999 M (3)S FmE 4821 0 :M f148 sf ( )S 4823 0 :M FrMacBegin B 0 FmP F FmOP 86.108 300.499 M ( )S FmE 4824 0 :M f237 sf ( )S 4826 0 :M FrMacBegin B 0 FmP F FmOP 88.608 300.499 M (\254)S FmE 4826 0 :M f148 sf ( )S 4828 0 :M FrMacBegin B 0 FmP F FmOP 98.477 300.499 M ( [ ?, \(0, 0, 1\), ? ] and )S FmE 4829 0 :M f203 sf ( )S 4831 0 :M FrMacBegin B 0 FmP F FmOP 182.603 300.499 M (C)S FmE 4831 0 :M f276 sf ( )S 4833 0 :M FrMacBegin B 0 FmP F FmOP 189.272 302.999 M (3)S FmE 4833 0 :M f148 sf ( )S 4835 0 :M FrMacBegin B 0 FmP F FmOP 193.272 300.499 M ( )S FmE 4836 0 :M f237 sf ( )S 4838 0 :M FrMacBegin B 0 FmP F FmOP 195.772 300.499 M (\254)S FmE 4838 0 :M f148 sf ( )S 4840 0 :M FrMacBegin B 0 FmP F FmOP 205.641 300.499 M ( )S FmE 4841 0 :M f203 sf ( )S 4843 0 :M FrMacBegin B 0 FmP F FmOP 208.141 300.499 M (max)S FmE 4843 0 :M f148 sf ( )S 4845 0 :M FrMacBegin B 0 FmP F FmOP 224.798 300.499 M ([\(0, 0, 1\), \(1, 0, 0\)] = \(1, 0, 1\).)S FmE 4846 0 :M f203 sf ( )S 4848 0 :M FrMacBegin B 0 FmP F FmOP 58 316.999 M (e)S FmE 4848 0 :M f276 sf ( )S 4850 0 :M FrMacBegin B 0 FmP F FmOP 62.438 319.499 M (23)S FmE 4850 0 :M f148 sf ( )S 4852 0 :M FrMacBegin B 0 FmP F FmOP 70.438 316.999 M (: )S FmE 4853 0 :M f203 sf ( )S 4855 0 :M FrMacBegin B 0 FmP F FmOP 75.717 316.999 M (P)S FmE 4855 0 :M f276 sf ( )S 4857 0 :M FrMacBegin B 0 FmP F FmOP 81.825 319.499 M (2)S FmE 4857 0 :M f148 sf ( )S 4859 0 :M FrMacBegin B 0 FmP F FmOP 85.825 316.999 M ( sends message )S FmE 4860 0 :M f203 sf ( )S 4862 0 :M FrMacBegin B 0 FmP F FmOP 149.414 316.999 M (m)S FmE 4862 0 :M f276 sf ( )S 4864 0 :M FrMacBegin B 0 FmP F FmOP 156.633 319.499 M (2,2)S FmE 4864 0 :M f148 sf ( )S 4866 0 :M FrMacBegin B 0 FmP F FmOP 166.633 316.999 M ( to )S FmE 4867 0 :M f203 sf ( )S 4869 0 :M FrMacBegin B 0 FmP F FmOP 179.412 316.999 M (P)S FmE 4869 0 :M f276 sf ( )S 4871 0 :M FrMacBegin B 0 FmP F FmOP 185.52 319.499 M (1)S FmE 4871 0 :M f148 sf ( )S 4873 0 :M FrMacBegin B 0 FmP F FmOP 189.52 316.999 M (. )S FmE 4874 0 :M f203 sf ( )S 4876 0 :M FrMacBegin B 0 FmP F FmOP 194.52 316.999 M (C)S FmE 4876 0 :M f276 sf ( )S 4878 0 :M FrMacBegin B 0 FmP F FmOP 201.19 319.499 M (2)S FmE 4878 0 :M f148 sf ( )S 4880 0 :M FrMacBegin B 0 FmP F FmOP 205.19 316.999 M ( )S FmE 4881 0 :M f237 sf ( )S 4883 0 :M FrMacBegin B 0 FmP F FmOP 207.69 316.999 M (\254)S FmE 4883 0 :M f148 sf ( )S 4885 0 :M FrMacBegin B 0 FmP F FmOP 217.558 316.999 M ( \(0, 2, 1\); )S FmE 4886 0 :M f203 sf ( )S 4888 0 :M FrMacBegin B 0 FmP F FmOP 256.992 316.999 M (t)S FmE 4888 0 :M f276 sf ( )S 4890 0 :M FrMacBegin B 0 FmP F FmOP 259.77 312.999 M (2,2)S FmE 4890 0 :M f148 sf ( )S 4892 0 :M FrMacBegin B 0 FmP F FmOP 269.77 316.999 M ( )S FmE 4893 0 :M f237 sf ( )S 4895 0 :M FrMacBegin B 0 FmP F FmOP 272.27 316.999 M (\254)S FmE 4895 0 :M f148 sf ( )S 4897 0 :M FrMacBegin B 0 FmP F FmOP 282.138 316.999 M ( \(0, 2, 1\), )S FmE 4898 0 :M f203 sf ( )S 4900 0 :M FrMacBegin B 0 FmP F FmOP 320.942 316.999 M (V)S FmE 4900 0 :M f276 sf ( )S 4902 0 :M FrMacBegin B 0 FmP F FmOP 327.05 312.999 M (2,2)S FmE 4902 0 :M f148 sf ( )S 4904 0 :M FrMacBegin B 0 FmP F FmOP 337.05 316.999 M ( )S FmE 4905 0 :M f237 sf ( )S 4907 0 :M FrMacBegin B 0 FmP F FmOP 339.55 316.999 M (\254)S FmE 4907 0 :M f148 sf ( )S 4909 0 :M FrMacBegin B 0 FmP F FmOP 349.418 316.999 M ( [ \(0, 1, 1\), ?, ? ];)S FmE 4910 0 :M f203 sf ( )S 4912 0 :M FrMacBegin B 0 FmP F FmOP 416.884 316.999 M ( )S -0.352 N (V)S FmE 4912 0 :M f276 sf ( )S 4914 0 :M FrMacBegin B 0 FmP F FmOP 425.141 319.499 M (2)S FmE 4914 0 :M f148 sf ( )S 4916 0 :M FrMacBegin B 0 FmP F FmOP 429.141 316.999 M ( )S FmE 4917 0 :M f237 sf ( )S 4919 0 :M FrMacBegin B 0 FmP F FmOP 431.641 316.999 M (\254)S FmE 4919 0 :M f148 sf ( )S 4921 0 :M FrMacBegin B 0 FmP F FmOP 441.509 316.999 M ( [ \(0, 2, 1\), ?, ? ])S FmE 4922 0 :M f203 sf ( )S 4924 0 :M FrMacBegin B 0 FmP F FmOP 58 333.499 M (e)S FmE 4924 0 :M f276 sf ( )S 4926 0 :M FrMacBegin B 0 FmP F FmOP 62.438 335.999 M (12)S FmE 4926 0 :M f148 sf ( )S 4928 0 :M FrMacBegin B 0 FmP F FmOP 70.438 333.499 M (: )S FmE 4929 0 :M f203 sf ( )S 4931 0 :M FrMacBegin B 0 FmP F FmOP 75.717 333.499 M (P)S FmE 4931 0 :M f276 sf ( )S 4933 0 :M FrMacBegin B 0 FmP F FmOP 81.825 335.999 M (1)S FmE 4933 0 :M f148 sf ( )S 4935 0 :M FrMacBegin B 0 FmP F FmOP 85.825 333.499 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 4936 0 :M f203 sf ( )S 4938 0 :M FrMacBegin B 0 FmP F FmOP 162.043 333.499 M (m)S FmE 4938 0 :M f276 sf ( )S 4940 0 :M FrMacBegin B 0 FmP F FmOP 169.263 335.999 M (2,2)S FmE 4940 0 :M f148 sf ( )S 4942 0 :M FrMacBegin B 0 FmP F FmOP 179.263 333.499 M ( from )S FmE 4943 0 :M f203 sf ( )S 4945 0 :M FrMacBegin B 0 FmP F FmOP 203.696 333.499 M (P)S FmE 4945 0 :M f276 sf ( )S 4947 0 :M FrMacBegin B 0 FmP F FmOP 209.805 335.999 M (2)S FmE 4947 0 :M f148 sf ( )S 4949 0 :M FrMacBegin B 0 FmP F FmOP 213.805 333.499 M (. But )S FmE 4950 0 :M f203 sf ( )S 4952 0 :M FrMacBegin B 0 FmP F FmOP 235.401 333.499 M (V)S FmE 4952 0 :M f276 sf ( )S 4954 0 :M FrMacBegin B 0 FmP F FmOP 241.51 329.499 M (2,2)S FmE 4954 0 :M f148 sf ( )S 4956 0 :M FrMacBegin B 0 FmP F FmOP 251.51 333.499 M ([1] = \(0, 1, 1\) <)S -3.333 N (/)S 3.333 N (\(1, 0, 0\) = )S FmE 4957 0 :M f203 sf ( )S 4959 0 :M FrMacBegin B 0 FmP F FmOP 358.673 333.499 M (C)S FmE 4959 0 :M f276 sf ( )S 4961 0 :M FrMacBegin B 0 FmP F FmOP 365.343 335.999 M (1)S FmE 4961 0 :M f148 sf ( )S 4963 0 :M FrMacBegin B 0 FmP F FmOP 369.343 333.499 M (, so the message is queued.)S FmE 4964 0 :M f203 sf ( )S 4966 0 :M FrMacBegin B 0 FmP F FmOP 58 349.998 M (e)S FmE 4966 0 :M f276 sf ( )S 4968 0 :M FrMacBegin B 0 FmP F FmOP 62.438 352.498 M (13)S FmE 4968 0 :M f148 sf ( )S 4970 0 :M FrMacBegin B 0 FmP F FmOP 70.438 349.998 M (: )S FmE 4971 0 :M f203 sf ( )S 4973 0 :M FrMacBegin B 0 FmP F FmOP 75.717 349.998 M (P)S FmE 4973 0 :M f276 sf ( )S 4975 0 :M FrMacBegin B 0 FmP F FmOP 81.825 352.498 M (1)S FmE 4975 0 :M f148 sf ( )S 4977 0 :M FrMacBegin B 0 FmP F FmOP 85.825 349.998 M ( recei)S -0.251 N (v)S -0.151 N (es message )S FmE 4978 0 :M f203 sf ( )S 4980 0 :M FrMacBegin B 0 FmP F FmOP 159.543 349.998 M (m)S FmE 4980 0 :M f276 sf ( )S 4982 0 :M FrMacBegin B 0 FmP F FmOP 166.763 352.498 M (2,1)S FmE 4982 0 :M f148 sf ( )S 4984 0 :M FrMacBegin B 0 FmP F FmOP 176.763 349.998 M ( from )S FmE 4985 0 :M f203 sf ( )S 4987 0 :M FrMacBegin B 0 FmP F FmOP 201.196 349.998 M (P)S FmE 4987 0 :M f276 sf ( )S 4989 0 :M FrMacBegin B 0 FmP F FmOP 207.305 352.498 M (2)S FmE 4989 0 :M f148 sf ( )S 4991 0 :M FrMacBegin B 0 FmP F FmOP 211.305 349.998 M (. )S -0.552 N (As )S FmE 4992 0 :M f203 sf ( )S 4994 0 :M FrMacBegin B 0 FmP F FmOP 229.01 349.998 M (V)S FmE 4994 0 :M f276 sf ( )S 4996 0 :M FrMacBegin B 0 FmP F FmOP 235.118 345.998 M (2,1)S FmE 4996 0 :M f148 sf ( )S 4998 0 :M FrMacBegin B 0 FmP F FmOP 245.118 349.998 M ([1] = [ ?, ?, ? ][1] is uninitialized, the message is accepted.)S FmE 4999 0 :M f203 sf ( )S 5001 0 :M FrMacBegin B 0 FmP F FmOP 76 363.832 M (V)S FmE 5001 0 :M f276 sf ( )S 5003 0 :M FrMacBegin B 0 FmP F FmOP 82.108 366.332 M (1)S FmE 5003 0 :M f148 sf ( )S 5005 0 :M FrMacBegin B 0 FmP F FmOP 86.108 363.832 M ( )S FmE 5006 0 :M f237 sf ( )S 5008 0 :M FrMacBegin B 0 FmP F FmOP 88.608 363.832 M (\254)S FmE 5008 0 :M f148 sf ( )S 5010 0 :M FrMacBegin B 0 FmP F FmOP 98.477 363.832 M ( [ ?, ?, \(1, 0, 0\) ] and )S FmE 5011 0 :M f203 sf ( )S 5013 0 :M FrMacBegin B 0 FmP F FmOP 182.603 363.832 M (C)S FmE 5013 0 :M f276 sf ( )S 5015 0 :M FrMacBegin B 0 FmP F FmOP 189.272 366.332 M (1)S FmE 5015 0 :M f148 sf ( )S 5017 0 :M FrMacBegin B 0 FmP F FmOP 193.272 363.832 M ( )S FmE 5018 0 :M f237 sf ( )S 5020 0 :M FrMacBegin B 0 FmP F FmOP 195.772 363.832 M (\254)S FmE 5020 0 :M f148 sf ( )S 5022 0 :M FrMacBegin B 0 FmP F FmOP 205.641 363.832 M ( )S FmE 5023 0 :M f203 sf ( )S 5025 0 :M FrMacBegin B 0 FmP F FmOP 208.141 363.832 M (max)S FmE 5025 0 :M f148 sf ( )S 5027 0 :M FrMacBegin B 0 FmP F FmOP 224.798 363.832 M ([\(1, 0, 0\), \(0, 1, 1\)] = \(1, 1, 1\).)S 76 380.332 M (The message on the queue is no)S -0.251 N (w check)S -0.1 N (ed. )S -0.552 N (As )S FmE 5028 0 :M f203 sf ( )S 5030 0 :M FrMacBegin B 0 FmP F FmOP 263.007 380.332 M (V)S FmE 5030 0 :M f276 sf ( )S 5032 0 :M FrMacBegin B 0 FmP F FmOP 269.115 376.332 M (2,2)S FmE 5032 0 :M f148 sf ( )S 5034 0 :M FrMacBegin B 0 FmP F FmOP 279.115 380.332 M ([1] = \(0, 1, 1\) < \(1, 1, 1\) = )S FmE 5035 0 :M f203 sf ( )S 5037 0 :M FrMacBegin B 0 FmP F FmOP 386 380.332 M (C)S FmE 5037 0 :M f276 sf ( )S 5039 0 :M FrMacBegin B 0 FmP F FmOP 392.67 382.832 M (1)S FmE 5039 0 :M f148 sf ( )S 5041 0 :M FrMacBegin B 0 FmP F FmOP 396.67 380.332 M (, the message is no)S -0.251 N (w accepted.)S FmE 5042 0 :M f203 sf ( )S 5044 0 :M FrMacBegin B 0 FmP F FmOP 76 394.165 M (V)S FmE 5044 0 :M f276 sf ( )S 5046 0 :M FrMacBegin B 0 FmP F FmOP 82.108 396.665 M (1)S FmE 5046 0 :M f148 sf ( )S 5048 0 :M FrMacBegin B 0 FmP F FmOP 86.108 394.165 M ( )S FmE 5049 0 :M f237 sf ( )S 5051 0 :M FrMacBegin B 0 FmP F FmOP 88.608 394.165 M (\254)S FmE 5051 0 :M f148 sf ( )S 5053 0 :M FrMacBegin B 0 FmP F FmOP 98.477 394.165 M ( [ ?, ?, \(1, 0, 0\) ] and )S FmE 5054 0 :M f203 sf ( )S 5056 0 :M FrMacBegin B 0 FmP F FmOP 182.603 394.165 M (C)S FmE 5056 0 :M f276 sf ( )S 5058 0 :M FrMacBegin B 0 FmP F FmOP 189.272 396.665 M (1)S FmE 5058 0 :M f148 sf ( )S 5060 0 :M FrMacBegin B 0 FmP F FmOP 193.272 394.165 M ( is set to \(1, 2, 1\).)S FmE 58 73 468 118 rC 5061 0 :M FrMacBegin 58 73.167 468 117.333 FmKp B 0 FmP F FmOP 112 91.971 FmB 378 0 FmL 2 1 FmSo 111.333 127.971 FmB 378 0 FmL 2 1 FmSo 112 172.971 FmB 378 0 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 259.5 92.137 FmAF T 0 360 4.5 4.5 0 259.5 92.137 2 1 F FmAP 0 360 4.5 4.5 0 T 200.833 128.137 FmAF T 0 360 4.5 4.5 0 200.833 128.137 2 1 F FmAP 0 360 4.5 4.5 0 T 251.5 128.137 FmAF T 0 360 4.5 4.5 0 251.5 128.137 2 1 F FmAP 0 360 4.5 4.5 0 T 163.5 174.137 FmAF T 0 360 4.5 4.5 0 163.5 174.137 2 1 F FmAP 0 360 4.167 4.5 0 T 342.5 173.523 FmAF T 0 360 4.167 4.5 0 342.5 173.523 2 1 F FmAP 0 360 4.5 4.5 0 T 414.833 92.804 FmAF T 0 360 4.5 4.5 0 414.833 92.804 2 1 F FmAP FmE 5061 0 :M f289 sf ( )S 5064 0 :M FrMacBegin 58 73.167 468 117.333 FmKp B 0 FmP F FmOP 91.333 92.338 M (P)S FmE 5064 0 :M f148 sf ( )S 5066 0 :M FrMacBegin 58 73.167 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 95.338 M 0.96 0.96 scale (1)S FmR FmE 5067 0 :M f289 sf ( )S 5070 0 :M FrMacBegin 58 73.167 468 117.333 FmKp B 0 FmP F FmOP 91.333 129.671 M (P)S FmE 5070 0 :M f148 sf ( )S 5072 0 :M FrMacBegin 58 73.167 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 132.671 M 0.96 0.96 scale (2)S FmR FmE 5072 0 :M f289 sf ( )S 5075 0 :M FrMacBegin 58 73.167 468 117.333 FmKp B 0 FmP F FmOP 91.333 176.338 M (P)S FmE 5075 0 :M f148 sf ( )S 5077 0 :M FrMacBegin 58 73.167 468 117.333 FmKp B 0 FmP F FmOP FmG 98.663 179.338 M 0.96 0.96 scale (3)S FmR FmG 258.126 82.083 M 0.96 0.96 scale (e11)S FmR FmG 198.667 120.671 M 0.96 0.96 scale (e21)S FmR FmG 252 120.671 M 0.96 0.96 scale (e22)S FmR FmG 147.333 165.338 M 0.96 0.96 scale (e31)S FmR FmG 340.667 166.057 M 0.96 0.96 scale (e32)S FmR FmG 408.667 85.338 M 0.96 0.96 scale (e12)S FmR 448.924 95.537 FmB -0.549 -3.427 FmL 12.501 1.512 FmL -11.403 5.342 FmL 1 FmS 448.924 95.537 FmB -0.549 -3.427 FmL 12.501 1.512 FmL -11.403 5.342 FmL FmFl 256.667 126.338 FmB 191.764 -30.722 FmL 2 1 FmSo 329.842 160.32 FmB 2.373 -2.533 FmL 6.463 10.808 FmL -11.208 -5.741 FmL 1 FmS 329.842 160.32 FmB 2.373 -2.533 FmL 6.463 10.808 FmL -11.208 -5.741 FmL FmFl 256 91.167 FmB 73.477 68.812 FmL 2 1 FmSo 190.319 141.609 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL 1 FmS 190.319 141.609 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL FmFl 165.333 171.004 FmB 24.662 -29.014 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 398.167 128.137 FmAF T 0 360 4.5 4.5 0 398.167 128.137 2 1 F FmAP FmG 404.667 136.671 M 0.96 0.96 scale (e23)S FmR 406.639 109.538 FmB -3.043 -1.67 FmL 8.865 -8.943 FmL -2.779 12.282 FmL 1 FmS 406.639 109.538 FmB -3.043 -1.67 FmL 8.865 -8.943 FmL -2.779 12.282 FmL FmFl 397.333 126.5 FmB 9.065 -16.524 FmL 2 1 FmSo FmG 464 86.004 M 0.96 0.96 scale (e13)S FmR 0 360 4.5 4.5 0 T 466.833 91.471 FmAF T 0 360 4.5 4.5 0 466.833 91.471 2 1 F FmAP FmE endp showpage %%PageTrailer %%Page: 9 9 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 9 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 5078 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 5078 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 5078 0 :M f148 sf ( )S 5080 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Chandy-Lamport Global State Recording Protocol)S (ECS 251 \320 Winter 2001)S 143.356 N (Page )S (9)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 5081 0 :M f175 sf ( )S 5085 0 :M FrMacBegin B 0 FmP F FmOP 97.173 72 M (Chandy-Lamport Global State Recording Pr)S -0.325 N (otocol)S FmE 5085 0 :M f263 sf ( )S 5088 0 :M FrMacBegin B 0 FmP F FmOP 58 104 M (Intr)S -0.217 N (oduction)S FmE 5088 0 :M f148 sf ( )S 5090 0 :M FrMacBegin B 0 FmP F FmOP 58 121.667 M (The goal of this distrib)S -0.2 N (uted algorithm is to capture a consistent global state. It assumes all communication channels )S 58 133.667 M (are FIFO. It uses a distinguished message called a )S FmE 5091 0 :M f203 sf ( )S 5093 0 :M FrMacBegin B 0 FmP F FmOP 260.144 133.667 M (mark)S -0.1 N (er)S FmE 5093 0 :M f148 sf ( )S 5095 0 :M FrMacBegin B 0 FmP F FmOP 288.918 133.667 M ( to start the algorithm.)S FmE 5096 0 :M f263 sf ( )S 5099 0 :M FrMacBegin B 0 FmP F FmOP 58 159 M (Pr)S -0.217 N (otocol)S FmE 5099 0 :M f319 sf ( )S 5101 0 :M FrMacBegin B 0 FmP F FmOP 58 176.667 M (P)S FmE 5101 0 :M f332 sf ( )S 5103 0 :M FrMacBegin B 0 FmP F FmOP 64.108 179.167 M (i)S FmE 5103 0 :M f345 sf ( )S 5105 0 :M FrMacBegin B 0 FmP F FmOP 66.331 176.667 M ( sends mark)S -0.1 N (er)S FmE 5106 0 :M f148 sf ( )S 5108 0 :M FrMacBegin B 0 FmP F FmOP 58 190.5 M (1.)S FmE 5108 0 :M f203 sf ( )S 5110 0 :M FrMacBegin B 0 FmP F FmOP 76 190.5 M (Pi)S FmE 5111 0 :M f148 sf ( )S 5113 0 :M FrMacBegin B 0 FmP F FmOP 84.887 190.5 M ( records its local state )S FmE 5113 0 :M f203 sf ( )S 5115 0 :M FrMacBegin B 0 FmP F FmOP 176.51 190.5 M (LS)S FmE 5116 0 :M f250 sf ( )S 5118 0 :M FrMacBegin B 0 FmP F FmOP 187.069 193 M (i)S FmE 5118 0 :M f148 sf ( )S 5120 0 :M FrMacBegin B 0 FmP F FmOP 58 204.633 M (2.)S 10.5 N (F)S -0.151 N (or each )S FmE 5120 0 :M f203 sf ( )S 5122 0 :M FrMacBegin B 0 FmP F FmOP 113.051 204.633 M (C)S FmE 5123 0 :M f250 sf ( )S 5125 0 :M FrMacBegin B 0 FmP F FmOP 119.721 207.133 M (ij)S FmE 5125 0 :M f148 sf ( )S 5127 0 :M FrMacBegin B 0 FmP F FmOP 124.166 204.633 M ( on which )S FmE 5127 0 :M f203 sf ( )S 5129 0 :M FrMacBegin B 0 FmP F FmOP 166.102 204.633 M (P)S FmE 5130 0 :M f250 sf ( )S 5132 0 :M FrMacBegin B 0 FmP F FmOP 172.21 207.133 M (i)S FmE 5132 0 :M f148 sf ( )S 5134 0 :M FrMacBegin B 0 FmP F FmOP 174.433 204.633 M ( has not already sent a mark)S -0.1 N (er)S -0.4 N (, )S FmE 5134 0 :M f203 sf ( )S 5136 0 :M FrMacBegin B 0 FmP F FmOP 298.315 204.633 M (P)S FmE 5137 0 :M f250 sf ( )S 5139 0 :M FrMacBegin B 0 FmP F FmOP 304.423 207.133 M (i)S FmE 5139 0 :M f148 sf ( )S 5141 0 :M FrMacBegin B 0 FmP F FmOP 306.646 204.633 M ( sends a mark)S -0.1 N (er )S FmE 5141 0 :M f203 sf ( )S 5143 0 :M FrMacBegin B 0 FmP F FmOP 371.512 204.633 M (befor)S -0.371 N (e)S FmE 5144 0 :M f148 sf ( )S 5146 0 :M FrMacBegin B 0 FmP F FmOP 396.685 204.633 M ( sending other messages.)S FmE 5146 0 :M f319 sf ( )S 5148 0 :M FrMacBegin B 0 FmP F FmOP 58 218.766 M (P)S FmE 5149 0 :M f332 sf ( )S 5151 0 :M FrMacBegin B 0 FmP F FmOP 64.108 221.266 M (i)S FmE 5151 0 :M f345 sf ( )S 5153 0 :M FrMacBegin B 0 FmP F FmOP 66.331 218.766 M ( r)S -0.181 N (ecei)S -0.1 N (v)S -0.1 N (es mark)S -0.1 N (er fr)S -0.181 N (om )S FmE 5153 0 :M f319 sf ( )S 5155 0 :M FrMacBegin B 0 FmP F FmOP 162.825 218.766 M (P)S FmE 5156 0 :M f332 sf ( )S 5158 0 :M FrMacBegin B 0 FmP F FmOP 168.934 221.266 M (j)S FmE 5158 0 :M f148 sf ( )S 5160 0 :M FrMacBegin B 0 FmP F FmOP 58 232.6 M (1.)S 10.5 N (If )S FmE 5160 0 :M f203 sf ( )S 5162 0 :M FrMacBegin B 0 FmP F FmOP 85.155 232.6 M (P)S FmE 5163 0 :M f250 sf ( )S 5165 0 :M FrMacBegin B 0 FmP F FmOP 91.264 235.1 M (i)S FmE 5165 0 :M f148 sf ( )S 5167 0 :M FrMacBegin B 0 FmP F FmOP 93.486 232.6 M ( has )S FmE 5167 0 :M f203 sf ( )S 5169 0 :M FrMacBegin B 0 FmP F FmOP 111.814 232.6 M (not)S FmE 5170 0 :M f148 sf ( )S 5172 0 :M FrMacBegin B 0 FmP F FmOP 124.592 232.6 M ( recorded its state:)S 76 246.433 M (a.)S 11.062 N (Record the state of )S FmE 5172 0 :M f203 sf ( )S 5174 0 :M FrMacBegin B 0 FmP F FmOP 171.742 246.433 M (C)S FmE 5175 0 :M f250 sf ( )S 5177 0 :M FrMacBegin B 0 FmP F FmOP 178.412 248.933 M (ji)S FmE 5177 0 :M f148 sf ( )S 5179 0 :M FrMacBegin B 0 FmP F FmOP 182.857 246.433 M ( as empty)S 76 260.266 M (b)S -0.4 N (.)S 10.9 N (Send the mark)S -0.1 N (er as described abo)S -0.151 N (v)S -0.151 N (e)S 58 272.566 M (2.)S 10.5 N (If )S FmE 5179 0 :M f203 sf ( )S 5181 0 :M FrMacBegin B 0 FmP F FmOP 85.155 272.566 M (P)S FmE 5182 0 :M f250 sf ( )S 5184 0 :M FrMacBegin B 0 FmP F FmOP 91.264 275.066 M (i)S FmE 5184 0 :M f148 sf ( )S 5186 0 :M FrMacBegin B 0 FmP F FmOP 93.486 272.566 M ( has recorded its state )S FmE 5186 0 :M f203 sf ( )S 5188 0 :M FrMacBegin B 0 FmP F FmOP 182.053 272.566 M (LS)S FmE 5189 0 :M f250 sf ( )S 5191 0 :M FrMacBegin B 0 FmP F FmOP 192.612 275.066 M (i)S FmE 5191 0 :M f148 sf ( )S 5193 0 :M FrMacBegin B 0 FmP F FmOP 76 286.7 M (a.)S 11.062 N (Record the state of )S FmE 5193 0 :M f203 sf ( )S 5195 0 :M FrMacBegin B 0 FmP F FmOP 171.742 286.7 M (C)S FmE 5196 0 :M f250 sf ( )S 5198 0 :M FrMacBegin B 0 FmP F FmOP 178.412 289.2 M (ji)S FmE 5198 0 :M f148 sf ( )S 5200 0 :M FrMacBegin B 0 FmP F FmOP 182.857 286.7 M ( to be the sequence of messages recei)S -0.251 N (v)S -0.151 N (ed between the computation of )S FmE 5200 0 :M f203 sf ( )S 5202 0 :M FrMacBegin B 0 FmP F FmOP 462.327 286.7 M (LS)S FmE 5203 0 :M f250 sf ( )S 5205 0 :M FrMacBegin B 0 FmP F FmOP 472.886 289.2 M (i)S FmE 5205 0 :M f148 sf ( )S 5207 0 :M FrMacBegin B 0 FmP F FmOP 475.109 286.7 M ( and the )S 94 300.533 M (mark)S -0.1 N (er from )S FmE 5207 0 :M f203 sf ( )S 5209 0 :M FrMacBegin B 0 FmP F FmOP 146.644 300.533 M (C)S FmE 5210 0 :M f250 sf ( )S 5212 0 :M FrMacBegin B 0 FmP F FmOP 153.314 303.033 M (ji)S FmE 5212 0 :M f148 sf ( )S 5214 0 :M FrMacBegin B 0 FmP F FmOP 157.759 300.533 M (.)S FmE endp showpage %%PageTrailer %%Page: 10 10 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 10 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 5214 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 5214 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 5214 0 :M f148 sf ( )S 5216 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Chandy-Lamport Global State Recording Protocol)S (ECS 251 \320 Winter 2001)S 138.356 N (Page )S (10)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 5217 0 :M f263 sf ( )S 5220 0 :M FrMacBegin B 0 FmP F FmOP 58 68 M (Example)S FmE 5220 0 :M f148 sf ( )S 5222 0 :M FrMacBegin B 0 FmP F FmOP 58 201 M (Here, all processes are connected by communications channels )S FmE 5222 0 :M f203 sf ( )S 5224 0 :M FrMacBegin B 0 FmP F FmOP 312.045 201 M (C)S FmE 5225 0 :M f250 sf ( )S 5227 0 :M FrMacBegin B 0 FmP F FmOP 318.715 203.5 M (ij)S FmE 5227 0 :M f148 sf ( )S 5229 0 :M FrMacBegin B 0 FmP F FmOP 323.161 201 M (. Messages being sent o)S -0.151 N (v)S -0.151 N (er the channels are repre-)S 58 214.833 M (sented by arro)S -0.251 N (ws between the processes.)S 58 226.833 M (Snapshot )S FmE 5229 0 :M f203 sf ( )S 5231 0 :M FrMacBegin B 0 FmP F FmOP 97.165 226.833 M (s)S FmE 5232 0 :M f276 sf ( )S 5234 0 :M FrMacBegin B 0 FmP F FmOP 101.054 229.333 M (1)S FmE 5234 0 :M f148 sf ( )S 5236 0 :M FrMacBegin B 0 FmP F FmOP 105.054 226.833 M (:)S FmE 5236 0 :M f203 sf ( )S 5238 0 :M FrMacBegin B 0 FmP F FmOP 58 240.667 M (P)S FmE 5239 0 :M f276 sf ( )S 5241 0 :M FrMacBegin B 0 FmP F FmOP 64.108 243.167 M (1)S FmE 5241 0 :M f148 sf ( )S 5243 0 :M FrMacBegin B 0 FmP F FmOP 68.108 240.667 M ( records )S FmE 5243 0 :M f203 sf ( )S 5245 0 :M FrMacBegin B 0 FmP F FmOP 102.53 240.667 M (LS)S FmE 5246 0 :M f276 sf ( )S 5248 0 :M FrMacBegin B 0 FmP F FmOP 113.089 243.167 M (1)S FmE 5248 0 :M f148 sf ( )S 5250 0 :M FrMacBegin B 0 FmP F FmOP 117.089 240.667 M (, sends mark)S -0.1 N (ers on )S FmE 5250 0 :M f203 sf ( )S 5252 0 :M FrMacBegin B 0 FmP F FmOP 193.905 240.667 M (C)S FmE 5253 0 :M f276 sf ( )S 5255 0 :M FrMacBegin B 0 FmP F FmOP 200.575 243.167 M (12)S FmE 5255 0 :M f148 sf ( )S 5257 0 :M FrMacBegin B 0 FmP F FmOP 208.575 240.667 M ( and )S FmE 5257 0 :M f203 sf ( )S 5259 0 :M FrMacBegin B 0 FmP F FmOP 228.014 240.667 M (C)S FmE 5260 0 :M f276 sf ( )S 5262 0 :M FrMacBegin B 0 FmP F FmOP 234.684 243.167 M (13)S FmE 5262 0 :M f203 sf ( )S 5264 0 :M FrMacBegin B 0 FmP F FmOP 58 254.5 M (P)S FmE 5264 0 :M f276 sf ( )S 5266 0 :M FrMacBegin B 0 FmP F FmOP 64.108 257 M (2)S FmE 5266 0 :M f148 sf ( )S 5268 0 :M FrMacBegin B 0 FmP F FmOP 68.108 254.5 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5269 0 :M f203 sf ( )S 5271 0 :M FrMacBegin B 0 FmP F FmOP 158.099 254.5 M (P)S FmE 5271 0 :M f276 sf ( )S 5273 0 :M FrMacBegin B 0 FmP F FmOP 164.207 257 M (1)S FmE 5273 0 :M f148 sf ( )S 5275 0 :M FrMacBegin B 0 FmP F FmOP 168.207 254.5 M ( on )S FmE 5276 0 :M f203 sf ( )S 5278 0 :M FrMacBegin B 0 FmP F FmOP 183.207 254.5 M (C)S FmE 5278 0 :M f276 sf ( )S 5280 0 :M FrMacBegin B 0 FmP F FmOP 189.877 257 M (12)S FmE 5280 0 :M f148 sf ( )S 5282 0 :M FrMacBegin B 0 FmP F FmOP 197.877 254.5 M (; it records its state )S FmE 5283 0 :M f203 sf ( )S 5285 0 :M FrMacBegin B 0 FmP F FmOP 275.902 254.5 M (LS)S FmE 5285 0 :M f276 sf ( )S 5287 0 :M FrMacBegin B 0 FmP F FmOP 286.461 257 M (2)S FmE 5287 0 :M f148 sf ( )S 5289 0 :M FrMacBegin B 0 FmP F FmOP 290.461 254.5 M (, records state of )S FmE 5290 0 :M f203 sf ( )S 5292 0 :M FrMacBegin B 0 FmP F FmOP 359.033 254.5 M (C)S FmE 5292 0 :M f276 sf ( )S 5294 0 :M FrMacBegin B 0 FmP F FmOP 365.703 257 M (12)S FmE 5294 0 :M f148 sf ( )S 5296 0 :M FrMacBegin B 0 FmP F FmOP 373.703 254.5 M ( as empty)S -0.652 N (, and sends mark)S -0.1 N (er on )S FmE 5297 0 :M f203 sf ( )S 5299 0 :M FrMacBegin B 0 FmP F FmOP 503.739 254.5 M (C)S FmE 5299 0 :M f276 sf ( )S 5301 0 :M FrMacBegin B 0 FmP F FmOP 510.409 257 M (21)S FmE 5301 0 :M f148 sf ( )S 5303 0 :M FrMacBegin B 0 FmP F FmOP 518.409 254.5 M ( )S 58 268.333 M (and )S FmE 5304 0 :M f203 sf ( )S 5306 0 :M FrMacBegin B 0 FmP F FmOP 74.938 268.333 M (C)S FmE 5306 0 :M f276 sf ( )S 5308 0 :M FrMacBegin B 0 FmP F FmOP 81.608 270.833 M (23)S FmE 5308 0 :M f203 sf ( )S 5310 0 :M FrMacBegin B 0 FmP F FmOP 58 282.166 M (P)S FmE 5311 0 :M f276 sf ( )S 5313 0 :M FrMacBegin B 0 FmP F FmOP 64.108 284.666 M (3)S FmE 5313 0 :M f148 sf ( )S 5315 0 :M FrMacBegin B 0 FmP F FmOP 68.108 282.166 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5315 0 :M f203 sf ( )S 5317 0 :M FrMacBegin B 0 FmP F FmOP 158.099 282.166 M (P)S FmE 5318 0 :M f276 sf ( )S 5320 0 :M FrMacBegin B 0 FmP F FmOP 164.207 284.666 M (1)S FmE 5320 0 :M f148 sf ( )S 5322 0 :M FrMacBegin B 0 FmP F FmOP 168.207 282.166 M ( on )S FmE 5322 0 :M f203 sf ( )S 5324 0 :M FrMacBegin B 0 FmP F FmOP 183.207 282.166 M (C)S FmE 5325 0 :M f276 sf ( )S 5327 0 :M FrMacBegin B 0 FmP F FmOP 189.877 284.666 M (13)S FmE 5327 0 :M f148 sf ( )S 5329 0 :M FrMacBegin B 0 FmP F FmOP 197.877 282.166 M (; it records its state )S FmE 5329 0 :M f203 sf ( )S 5331 0 :M FrMacBegin B 0 FmP F FmOP 275.902 282.166 M (LS)S FmE 5332 0 :M f276 sf ( )S 5334 0 :M FrMacBegin B 0 FmP F FmOP 286.461 284.666 M (3)S FmE 5334 0 :M f148 sf ( )S 5336 0 :M FrMacBegin B 0 FmP F FmOP 290.461 282.166 M (, records state of )S FmE 5336 0 :M f203 sf ( )S 5338 0 :M FrMacBegin B 0 FmP F FmOP 359.033 282.166 M (C)S FmE 5339 0 :M f276 sf ( )S 5341 0 :M FrMacBegin B 0 FmP F FmOP 365.703 284.666 M (13)S FmE 5341 0 :M f148 sf ( )S 5343 0 :M FrMacBegin B 0 FmP F FmOP 373.703 282.166 M ( as empty)S -0.652 N (, and sends mark)S -0.1 N (ers on )S FmE 5343 0 :M f203 sf ( )S 5345 0 :M FrMacBegin B 0 FmP F FmOP 505.128 282.166 M (C)S FmE 5346 0 :M f276 sf ( )S 5348 0 :M FrMacBegin B 0 FmP F FmOP 511.798 284.666 M (31)S FmE 5348 0 :M f148 sf ( )S 5350 0 :M FrMacBegin B 0 FmP F FmOP 519.798 282.166 M ( )S 58 296 M (and )S FmE 5350 0 :M f203 sf ( )S 5352 0 :M FrMacBegin B 0 FmP F FmOP 74.938 296 M (C)S FmE 5353 0 :M f276 sf ( )S 5355 0 :M FrMacBegin B 0 FmP F FmOP 81.608 298.5 M (32)S FmE 5355 0 :M f148 sf ( )S 5357 0 :M FrMacBegin B 0 FmP F FmOP 89.608 296 M (.)S FmE 5357 0 :M f203 sf ( )S 5359 0 :M FrMacBegin B 0 FmP F FmOP 58 309.833 M (P)S FmE 5360 0 :M f276 sf ( )S 5362 0 :M FrMacBegin B 0 FmP F FmOP 64.108 312.333 M (1)S FmE 5362 0 :M f148 sf ( )S 5364 0 :M FrMacBegin B 0 FmP F FmOP 68.108 309.833 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5364 0 :M f203 sf ( )S 5366 0 :M FrMacBegin B 0 FmP F FmOP 158.099 309.833 M (P)S FmE 5367 0 :M f276 sf ( )S 5369 0 :M FrMacBegin B 0 FmP F FmOP 164.207 312.333 M (2)S FmE 5369 0 :M f148 sf ( )S 5371 0 :M FrMacBegin B 0 FmP F FmOP 168.207 309.833 M ( on )S FmE 5371 0 :M f203 sf ( )S 5373 0 :M FrMacBegin B 0 FmP F FmOP 183.207 309.833 M (C)S FmE 5374 0 :M f276 sf ( )S 5376 0 :M FrMacBegin B 0 FmP F FmOP 189.877 312.333 M (21)S FmE 5376 0 :M f148 sf ( )S 5378 0 :M FrMacBegin B 0 FmP F FmOP 197.877 309.833 M (; as )S FmE 5378 0 :M f203 sf ( )S 5380 0 :M FrMacBegin B 0 FmP F FmOP 213.983 309.833 M (LS)S FmE 5381 0 :M f276 sf ( )S 5383 0 :M FrMacBegin B 0 FmP F FmOP 224.542 312.333 M (1)S FmE 5383 0 :M f148 sf ( )S 5385 0 :M FrMacBegin B 0 FmP F FmOP 228.542 309.833 M ( is recorded, it records the state of )S FmE 5385 0 :M f203 sf ( )S 5387 0 :M FrMacBegin B 0 FmP F FmOP 366.525 309.833 M (C)S FmE 5388 0 :M f276 sf ( )S 5390 0 :M FrMacBegin B 0 FmP F FmOP 373.195 312.333 M (21)S FmE 5390 0 :M f148 sf ( )S 5392 0 :M FrMacBegin B 0 FmP F FmOP 381.195 309.833 M ( as empty)S -0.652 N (.)S FmE 5392 0 :M f203 sf ( )S 5394 0 :M FrMacBegin B 0 FmP F FmOP 58 323.666 M (P)S FmE 5395 0 :M f276 sf ( )S 5397 0 :M FrMacBegin B 0 FmP F FmOP 64.108 326.166 M (1)S FmE 5397 0 :M f148 sf ( )S 5399 0 :M FrMacBegin B 0 FmP F FmOP 68.108 323.666 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5399 0 :M f203 sf ( )S 5401 0 :M FrMacBegin B 0 FmP F FmOP 158.099 323.666 M (P)S FmE 5402 0 :M f276 sf ( )S 5404 0 :M FrMacBegin B 0 FmP F FmOP 164.207 326.166 M (3)S FmE 5404 0 :M f148 sf ( )S 5406 0 :M FrMacBegin B 0 FmP F FmOP 168.207 323.666 M ( on )S FmE 5406 0 :M f203 sf ( )S 5408 0 :M FrMacBegin B 0 FmP F FmOP 183.207 323.666 M (C)S FmE 5409 0 :M f276 sf ( )S 5411 0 :M FrMacBegin B 0 FmP F FmOP 189.877 326.166 M (31)S FmE 5411 0 :M f148 sf ( )S 5413 0 :M FrMacBegin B 0 FmP F FmOP 197.877 323.666 M (; as )S FmE 5413 0 :M f203 sf ( )S 5415 0 :M FrMacBegin B 0 FmP F FmOP 213.983 323.666 M (LS)S FmE 5416 0 :M f276 sf ( )S 5418 0 :M FrMacBegin B 0 FmP F FmOP 224.542 326.166 M (1)S FmE 5418 0 :M f148 sf ( )S 5420 0 :M FrMacBegin B 0 FmP F FmOP 228.542 323.666 M ( is recorded, it records the state of )S FmE 5420 0 :M f203 sf ( )S 5422 0 :M FrMacBegin B 0 FmP F FmOP 366.525 323.666 M (C)S FmE 5423 0 :M f276 sf ( )S 5425 0 :M FrMacBegin B 0 FmP F FmOP 373.195 326.166 M (31)S FmE 5425 0 :M f148 sf ( )S 5427 0 :M FrMacBegin B 0 FmP F FmOP 381.195 323.666 M ( as empty)S -0.652 N (.)S FmE 5427 0 :M f203 sf ( )S 5429 0 :M FrMacBegin B 0 FmP F FmOP 58 337.5 M (P)S FmE 5430 0 :M f276 sf ( )S 5432 0 :M FrMacBegin B 0 FmP F FmOP 64.108 340 M (2)S FmE 5432 0 :M f148 sf ( )S 5434 0 :M FrMacBegin B 0 FmP F FmOP 68.108 337.5 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5434 0 :M f203 sf ( )S 5436 0 :M FrMacBegin B 0 FmP F FmOP 158.099 337.5 M (P)S FmE 5437 0 :M f276 sf ( )S 5439 0 :M FrMacBegin B 0 FmP F FmOP 164.207 340 M (3)S FmE 5439 0 :M f148 sf ( )S 5441 0 :M FrMacBegin B 0 FmP F FmOP 168.207 337.5 M ( on )S FmE 5441 0 :M f203 sf ( )S 5443 0 :M FrMacBegin B 0 FmP F FmOP 183.207 337.5 M (C)S FmE 5444 0 :M f276 sf ( )S 5446 0 :M FrMacBegin B 0 FmP F FmOP 189.877 340 M (32)S FmE 5446 0 :M f148 sf ( )S 5448 0 :M FrMacBegin B 0 FmP F FmOP 197.877 337.5 M (; as )S FmE 5448 0 :M f203 sf ( )S 5450 0 :M FrMacBegin B 0 FmP F FmOP 213.983 337.5 M (LS)S FmE 5451 0 :M f276 sf ( )S 5453 0 :M FrMacBegin B 0 FmP F FmOP 224.542 340 M (2)S FmE 5453 0 :M f148 sf ( )S 5455 0 :M FrMacBegin B 0 FmP F FmOP 228.542 337.5 M ( is recorded, it records the state of )S FmE 5455 0 :M f203 sf ( )S 5457 0 :M FrMacBegin B 0 FmP F FmOP 366.525 337.5 M (C)S FmE 5458 0 :M f276 sf ( )S 5460 0 :M FrMacBegin B 0 FmP F FmOP 373.195 340 M (32)S FmE 5460 0 :M f148 sf ( )S 5462 0 :M FrMacBegin B 0 FmP F FmOP 381.195 337.5 M ( as empty)S -0.652 N (.)S FmE 5462 0 :M f203 sf ( )S 5464 0 :M FrMacBegin B 0 FmP F FmOP 58 351.333 M (P)S FmE 5465 0 :M f276 sf ( )S 5467 0 :M FrMacBegin B 0 FmP F FmOP 64.108 353.833 M (3)S FmE 5467 0 :M f148 sf ( )S 5469 0 :M FrMacBegin B 0 FmP F FmOP 68.108 351.333 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5469 0 :M f203 sf ( )S 5471 0 :M FrMacBegin B 0 FmP F FmOP 158.099 351.333 M (P)S FmE 5472 0 :M f276 sf ( )S 5474 0 :M FrMacBegin B 0 FmP F FmOP 164.207 353.833 M (2)S FmE 5474 0 :M f148 sf ( )S 5476 0 :M FrMacBegin B 0 FmP F FmOP 168.207 351.333 M ( on )S FmE 5476 0 :M f203 sf ( )S 5478 0 :M FrMacBegin B 0 FmP F FmOP 183.207 351.333 M (C)S FmE 5479 0 :M f276 sf ( )S 5481 0 :M FrMacBegin B 0 FmP F FmOP 189.877 353.833 M (23)S FmE 5481 0 :M f148 sf ( )S 5483 0 :M FrMacBegin B 0 FmP F FmOP 197.877 351.333 M (; as )S FmE 5483 0 :M f203 sf ( )S 5485 0 :M FrMacBegin B 0 FmP F FmOP 213.983 351.333 M (LS)S FmE 5486 0 :M f276 sf ( )S 5488 0 :M FrMacBegin B 0 FmP F FmOP 224.542 353.833 M (3)S FmE 5488 0 :M f148 sf ( )S 5490 0 :M FrMacBegin B 0 FmP F FmOP 228.542 351.333 M ( is recorded, it records the state of )S FmE 5490 0 :M f203 sf ( )S 5492 0 :M FrMacBegin B 0 FmP F FmOP 366.525 351.333 M (C)S FmE 5493 0 :M f276 sf ( )S 5495 0 :M FrMacBegin B 0 FmP F FmOP 373.195 353.833 M (23)S FmE 5495 0 :M f148 sf ( )S 5497 0 :M FrMacBegin B 0 FmP F FmOP 381.195 351.333 M ( as empty)S -0.652 N (.)S 58 365.166 M (Snapshot )S FmE 5497 0 :M f203 sf ( )S 5499 0 :M FrMacBegin B 0 FmP F FmOP 97.165 365.166 M (s)S FmE 5500 0 :M f276 sf ( )S 5502 0 :M FrMacBegin B 0 FmP F FmOP 101.054 367.666 M (2)S FmE 5502 0 :M f148 sf ( )S 5504 0 :M FrMacBegin B 0 FmP F FmOP 105.054 365.166 M (: no)S -0.251 N (w messages are in transit on )S FmE 5504 0 :M f203 sf ( )S 5506 0 :M FrMacBegin B 0 FmP F FmOP 235.035 365.166 M (C)S FmE 5507 0 :M f276 sf ( )S 5509 0 :M FrMacBegin B 0 FmP F FmOP 241.705 367.666 M (12)S FmE 5509 0 :M f148 sf ( )S 5511 0 :M FrMacBegin B 0 FmP F FmOP 249.705 365.166 M ( and )S FmE 5511 0 :M f203 sf ( )S 5513 0 :M FrMacBegin B 0 FmP F FmOP 269.143 365.166 M (C)S FmE 5514 0 :M f276 sf ( )S 5516 0 :M FrMacBegin B 0 FmP F FmOP 275.813 367.666 M (21)S FmE 5516 0 :M f148 sf ( )S 5518 0 :M FrMacBegin B 0 FmP F FmOP 283.813 365.166 M (.)S FmE 5518 0 :M f203 sf ( )S 5520 0 :M FrMacBegin B 0 FmP F FmOP 58 378.999 M (P)S FmE 5521 0 :M f276 sf ( )S 5523 0 :M FrMacBegin B 0 FmP F FmOP 64.108 381.499 M (1)S FmE 5523 0 :M f148 sf ( )S 5525 0 :M FrMacBegin B 0 FmP F FmOP 68.108 378.999 M ( records )S FmE 5525 0 :M f203 sf ( )S 5527 0 :M FrMacBegin B 0 FmP F FmOP 102.53 378.999 M (LS)S FmE 5528 0 :M f276 sf ( )S 5530 0 :M FrMacBegin B 0 FmP F FmOP 113.089 381.499 M (1)S FmE 5530 0 :M f148 sf ( )S 5532 0 :M FrMacBegin B 0 FmP F FmOP 117.089 378.999 M (, sends mark)S -0.1 N (ers on )S FmE 5532 0 :M f203 sf ( )S 5534 0 :M FrMacBegin B 0 FmP F FmOP 193.905 378.999 M (C)S FmE 5535 0 :M f276 sf ( )S 5537 0 :M FrMacBegin B 0 FmP F FmOP 200.575 381.499 M (12)S FmE 5537 0 :M f148 sf ( )S 5539 0 :M FrMacBegin B 0 FmP F FmOP 208.575 378.999 M ( and )S FmE 5539 0 :M f203 sf ( )S 5541 0 :M FrMacBegin B 0 FmP F FmOP 228.014 378.999 M (C)S FmE 5542 0 :M f276 sf ( )S 5544 0 :M FrMacBegin B 0 FmP F FmOP 234.684 381.499 M (13)S FmE 5544 0 :M f203 sf ( )S 5546 0 :M FrMacBegin B 0 FmP F FmOP 58 392.833 M (P)S FmE 5546 0 :M f276 sf ( )S 5548 0 :M FrMacBegin B 0 FmP F FmOP 64.108 395.333 M (2)S FmE 5548 0 :M f148 sf ( )S 5550 0 :M FrMacBegin B 0 FmP F FmOP 68.108 392.833 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5551 0 :M f203 sf ( )S 5553 0 :M FrMacBegin B 0 FmP F FmOP 158.099 392.833 M (P)S FmE 5553 0 :M f276 sf ( )S 5555 0 :M FrMacBegin B 0 FmP F FmOP 164.207 395.333 M (1)S FmE 5555 0 :M f148 sf ( )S 5557 0 :M FrMacBegin B 0 FmP F FmOP 168.207 392.833 M ( on )S FmE 5558 0 :M f203 sf ( )S 5560 0 :M FrMacBegin B 0 FmP F FmOP 183.207 392.833 M (C)S FmE 5560 0 :M f276 sf ( )S 5562 0 :M FrMacBegin B 0 FmP F FmOP 189.877 395.333 M (12)S FmE 5562 0 :M f148 sf ( )S 5564 0 :M FrMacBegin B 0 FmP F FmOP 197.877 392.833 M ( after the message from )S FmE 5565 0 :M f203 sf ( )S 5567 0 :M FrMacBegin B 0 FmP F FmOP 294.21 392.833 M (P)S FmE 5567 0 :M f276 sf ( )S 5569 0 :M FrMacBegin B 0 FmP F FmOP 300.318 395.333 M (1)S FmE 5569 0 :M f148 sf ( )S 5571 0 :M FrMacBegin B 0 FmP F FmOP 304.318 392.833 M ( arri)S -0.251 N (v)S -0.151 N (es; it records its state )S FmE 5572 0 :M f203 sf ( )S 5574 0 :M FrMacBegin B 0 FmP F FmOP 411.64 392.833 M (LS)S FmE 5574 0 :M f276 sf ( )S 5576 0 :M FrMacBegin B 0 FmP F FmOP 422.199 395.333 M (2)S FmE 5576 0 :M f148 sf ( )S 5578 0 :M FrMacBegin B 0 FmP F FmOP 426.199 392.833 M (, records state of )S FmE 5579 0 :M f203 sf ( )S 5581 0 :M FrMacBegin B 0 FmP F FmOP 494.771 392.833 M (C)S FmE 5581 0 :M f276 sf ( )S 5583 0 :M FrMacBegin B 0 FmP F FmOP 501.441 395.333 M (12)S FmE 5583 0 :M f148 sf ( )S 5585 0 :M FrMacBegin B 0 FmP F FmOP 509.441 392.833 M ( as )S 58 406.666 M (empty)S -0.652 N (, and sends mark)S -0.1 N (er on )S FmE 5586 0 :M f203 sf ( )S 5588 0 :M FrMacBegin B 0 FmP F FmOP 174.709 406.666 M (C)S FmE 5588 0 :M f276 sf ( )S 5590 0 :M FrMacBegin B 0 FmP F FmOP 181.379 409.166 M (21)S FmE 5590 0 :M f148 sf ( )S 5592 0 :M FrMacBegin B 0 FmP F FmOP 189.379 406.666 M ( and )S FmE 5593 0 :M f203 sf ( )S 5595 0 :M FrMacBegin B 0 FmP F FmOP 208.817 406.666 M (C)S FmE 5595 0 :M f276 sf ( )S 5597 0 :M FrMacBegin B 0 FmP F FmOP 215.487 409.166 M (23)S FmE 5597 0 :M f203 sf ( )S 5599 0 :M FrMacBegin B 0 FmP F FmOP 58 420.499 M (P)S FmE 5600 0 :M f276 sf ( )S 5602 0 :M FrMacBegin B 0 FmP F FmOP 64.108 422.999 M (3)S FmE 5602 0 :M f148 sf ( )S 5604 0 :M FrMacBegin B 0 FmP F FmOP 68.108 420.499 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5604 0 :M f203 sf ( )S 5606 0 :M FrMacBegin B 0 FmP F FmOP 158.099 420.499 M (P)S FmE 5607 0 :M f276 sf ( )S 5609 0 :M FrMacBegin B 0 FmP F FmOP 164.207 422.999 M (1)S FmE 5609 0 :M f148 sf ( )S 5611 0 :M FrMacBegin B 0 FmP F FmOP 168.207 420.499 M ( on )S FmE 5611 0 :M f203 sf ( )S 5613 0 :M FrMacBegin B 0 FmP F FmOP 183.207 420.499 M (C)S FmE 5614 0 :M f276 sf ( )S 5616 0 :M FrMacBegin B 0 FmP F FmOP 189.877 422.999 M (13)S FmE 5616 0 :M f148 sf ( )S 5618 0 :M FrMacBegin B 0 FmP F FmOP 197.877 420.499 M (; it records its state )S FmE 5618 0 :M f203 sf ( )S 5620 0 :M FrMacBegin B 0 FmP F FmOP 275.902 420.499 M (LS)S FmE 5621 0 :M f276 sf ( )S 5623 0 :M FrMacBegin B 0 FmP F FmOP 286.461 422.999 M (3)S FmE 5623 0 :M f148 sf ( )S 5625 0 :M FrMacBegin B 0 FmP F FmOP 290.461 420.499 M (, records state of )S FmE 5625 0 :M f203 sf ( )S 5627 0 :M FrMacBegin B 0 FmP F FmOP 359.033 420.499 M (C)S FmE 5628 0 :M f276 sf ( )S 5630 0 :M FrMacBegin B 0 FmP F FmOP 365.703 422.999 M (13)S FmE 5630 0 :M f148 sf ( )S 5632 0 :M FrMacBegin B 0 FmP F FmOP 373.703 420.499 M ( as empty)S -0.652 N (, and sends mark)S -0.1 N (ers on )S FmE 5632 0 :M f203 sf ( )S 5634 0 :M FrMacBegin B 0 FmP F FmOP 505.128 420.499 M (C)S FmE 5635 0 :M f276 sf ( )S 5637 0 :M FrMacBegin B 0 FmP F FmOP 511.798 422.999 M (31)S FmE 5637 0 :M f148 sf ( )S 5639 0 :M FrMacBegin B 0 FmP F FmOP 519.798 420.499 M ( )S 58 434.333 M (and )S FmE 5639 0 :M f203 sf ( )S 5641 0 :M FrMacBegin B 0 FmP F FmOP 74.938 434.333 M (C)S FmE 5642 0 :M f276 sf ( )S 5644 0 :M FrMacBegin B 0 FmP F FmOP 81.608 436.833 M (32)S FmE 5644 0 :M f148 sf ( )S 5646 0 :M FrMacBegin B 0 FmP F FmOP 89.608 434.333 M (.)S FmE 5646 0 :M f203 sf ( )S 5648 0 :M FrMacBegin B 0 FmP F FmOP 58 448.166 M (P)S FmE 5649 0 :M f276 sf ( )S 5651 0 :M FrMacBegin B 0 FmP F FmOP 64.108 450.666 M (1)S FmE 5651 0 :M f148 sf ( )S 5653 0 :M FrMacBegin B 0 FmP F FmOP 68.108 448.166 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5653 0 :M f203 sf ( )S 5655 0 :M FrMacBegin B 0 FmP F FmOP 158.099 448.166 M (P)S FmE 5656 0 :M f276 sf ( )S 5658 0 :M FrMacBegin B 0 FmP F FmOP 164.207 450.666 M (2)S FmE 5658 0 :M f148 sf ( )S 5660 0 :M FrMacBegin B 0 FmP F FmOP 168.207 448.166 M ( on )S FmE 5660 0 :M f203 sf ( )S 5662 0 :M FrMacBegin B 0 FmP F FmOP 183.207 448.166 M (C)S FmE 5663 0 :M f276 sf ( )S 5665 0 :M FrMacBegin B 0 FmP F FmOP 189.877 450.666 M (21)S FmE 5665 0 :M f148 sf ( )S 5667 0 :M FrMacBegin B 0 FmP F FmOP 197.877 448.166 M (; as )S FmE 5667 0 :M f203 sf ( )S 5669 0 :M FrMacBegin B 0 FmP F FmOP 213.983 448.166 M (LS)S FmE 5670 0 :M f276 sf ( )S 5672 0 :M FrMacBegin B 0 FmP F FmOP 224.542 450.666 M (1)S FmE 5672 0 :M f148 sf ( )S 5674 0 :M FrMacBegin B 0 FmP F FmOP 228.542 448.166 M ( is recorded, and a message has arri)S -0.251 N (v)S -0.151 N (ed since )S FmE 5674 0 :M f203 sf ( )S 5676 0 :M FrMacBegin B 0 FmP F FmOP 409.709 448.166 M (LS)S FmE 5677 0 :M f276 sf ( )S 5679 0 :M FrMacBegin B 0 FmP F FmOP 420.268 450.666 M (1)S FmE 5679 0 :M f148 sf ( )S 5681 0 :M FrMacBegin B 0 FmP F FmOP 424.268 448.166 M ( w)S -0.1 N (as recorded, it records )S 58 461.999 M (the state of )S FmE 5681 0 :M f203 sf ( )S 5683 0 :M FrMacBegin B 0 FmP F FmOP 104.367 461.999 M (C)S FmE 5684 0 :M f276 sf ( )S 5686 0 :M FrMacBegin B 0 FmP F FmOP 111.037 464.499 M (21)S FmE 5686 0 :M f148 sf ( )S 5688 0 :M FrMacBegin B 0 FmP F FmOP 119.037 461.999 M ( as containing that message.)S FmE 5688 0 :M f203 sf ( )S 5690 0 :M FrMacBegin B 0 FmP F FmOP 58 475.832 M (P)S FmE 5691 0 :M f276 sf ( )S 5693 0 :M FrMacBegin B 0 FmP F FmOP 64.108 478.332 M (1)S FmE 5693 0 :M f148 sf ( )S 5695 0 :M FrMacBegin B 0 FmP F FmOP 68.108 475.832 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5695 0 :M f203 sf ( )S 5697 0 :M FrMacBegin B 0 FmP F FmOP 158.099 475.832 M (P)S FmE 5698 0 :M f276 sf ( )S 5700 0 :M FrMacBegin B 0 FmP F FmOP 164.207 478.332 M (3)S FmE 5700 0 :M f148 sf ( )S 5702 0 :M FrMacBegin B 0 FmP F FmOP 168.207 475.832 M ( on )S FmE 5702 0 :M f203 sf ( )S 5704 0 :M FrMacBegin B 0 FmP F FmOP 183.207 475.832 M (C)S FmE 5705 0 :M f276 sf ( )S 5707 0 :M FrMacBegin B 0 FmP F FmOP 189.877 478.332 M (31)S FmE 5707 0 :M f148 sf ( )S 5709 0 :M FrMacBegin B 0 FmP F FmOP 197.877 475.832 M (; as )S FmE 5709 0 :M f203 sf ( )S 5711 0 :M FrMacBegin B 0 FmP F FmOP 213.983 475.832 M (LS)S FmE 5712 0 :M f276 sf ( )S 5714 0 :M FrMacBegin B 0 FmP F FmOP 224.542 478.332 M (1)S FmE 5714 0 :M f148 sf ( )S 5716 0 :M FrMacBegin B 0 FmP F FmOP 228.542 475.832 M ( is recorded, it records the state of )S FmE 5716 0 :M f203 sf ( )S 5718 0 :M FrMacBegin B 0 FmP F FmOP 366.525 475.832 M (C)S FmE 5719 0 :M f276 sf ( )S 5721 0 :M FrMacBegin B 0 FmP F FmOP 373.195 478.332 M (31)S FmE 5721 0 :M f148 sf ( )S 5723 0 :M FrMacBegin B 0 FmP F FmOP 381.195 475.832 M ( as empty)S -0.652 N (.)S FmE 5723 0 :M f203 sf ( )S 5725 0 :M FrMacBegin B 0 FmP F FmOP 58 489.666 M (P)S FmE 5726 0 :M f276 sf ( )S 5728 0 :M FrMacBegin B 0 FmP F FmOP 64.108 492.166 M (2)S FmE 5728 0 :M f148 sf ( )S 5730 0 :M FrMacBegin B 0 FmP F FmOP 68.108 489.666 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5730 0 :M f203 sf ( )S 5732 0 :M FrMacBegin B 0 FmP F FmOP 158.099 489.666 M (P)S FmE 5733 0 :M f276 sf ( )S 5735 0 :M FrMacBegin B 0 FmP F FmOP 164.207 492.166 M (3)S FmE 5735 0 :M f148 sf ( )S 5737 0 :M FrMacBegin B 0 FmP F FmOP 168.207 489.666 M ( on )S FmE 5737 0 :M f203 sf ( )S 5739 0 :M FrMacBegin B 0 FmP F FmOP 183.207 489.666 M (C)S FmE 5740 0 :M f276 sf ( )S 5742 0 :M FrMacBegin B 0 FmP F FmOP 189.877 492.166 M (32)S FmE 5742 0 :M f148 sf ( )S 5744 0 :M FrMacBegin B 0 FmP F FmOP 197.877 489.666 M (; as )S FmE 5744 0 :M f203 sf ( )S 5746 0 :M FrMacBegin B 0 FmP F FmOP 213.983 489.666 M (LS)S FmE 5747 0 :M f276 sf ( )S 5749 0 :M FrMacBegin B 0 FmP F FmOP 224.542 492.166 M (2)S FmE 5749 0 :M f148 sf ( )S 5751 0 :M FrMacBegin B 0 FmP F FmOP 228.542 489.666 M ( is recorded, it records the state of )S FmE 5751 0 :M f203 sf ( )S 5753 0 :M FrMacBegin B 0 FmP F FmOP 366.525 489.666 M (C)S FmE 5754 0 :M f276 sf ( )S 5756 0 :M FrMacBegin B 0 FmP F FmOP 373.195 492.166 M (32)S FmE 5756 0 :M f148 sf ( )S 5758 0 :M FrMacBegin B 0 FmP F FmOP 381.195 489.666 M ( as empty)S -0.652 N (.)S FmE 5758 0 :M f203 sf ( )S 5760 0 :M FrMacBegin B 0 FmP F FmOP 58 503.499 M (P)S FmE 5761 0 :M f276 sf ( )S 5763 0 :M FrMacBegin B 0 FmP F FmOP 64.108 505.999 M (3)S FmE 5763 0 :M f148 sf ( )S 5765 0 :M FrMacBegin B 0 FmP F FmOP 68.108 503.499 M ( recei)S -0.251 N (v)S -0.151 N (es mark)S -0.1 N (er from )S FmE 5765 0 :M f203 sf ( )S 5767 0 :M FrMacBegin B 0 FmP F FmOP 158.099 503.499 M (P)S FmE 5768 0 :M f276 sf ( )S 5770 0 :M FrMacBegin B 0 FmP F FmOP 164.207 505.999 M (2)S FmE 5770 0 :M f148 sf ( )S 5772 0 :M FrMacBegin B 0 FmP F FmOP 168.207 503.499 M ( on )S FmE 5772 0 :M f203 sf ( )S 5774 0 :M FrMacBegin B 0 FmP F FmOP 183.207 503.499 M (C)S FmE 5775 0 :M f276 sf ( )S 5777 0 :M FrMacBegin B 0 FmP F FmOP 189.877 505.999 M (23)S FmE 5777 0 :M f148 sf ( )S 5779 0 :M FrMacBegin B 0 FmP F FmOP 197.877 503.499 M (; as )S FmE 5779 0 :M f203 sf ( )S 5781 0 :M FrMacBegin B 0 FmP F FmOP 213.983 503.499 M (LS)S FmE 5782 0 :M f276 sf ( )S 5784 0 :M FrMacBegin B 0 FmP F FmOP 224.542 505.999 M (3)S FmE 5784 0 :M f148 sf ( )S 5786 0 :M FrMacBegin B 0 FmP F FmOP 228.542 503.499 M ( is recorded, it records the state of )S FmE 5786 0 :M f203 sf ( )S 5788 0 :M FrMacBegin B 0 FmP F FmOP 366.525 503.499 M (C)S FmE 5789 0 :M f276 sf ( )S 5791 0 :M FrMacBegin B 0 FmP F FmOP 373.195 505.999 M (23)S FmE 5791 0 :M f148 sf ( )S 5793 0 :M FrMacBegin B 0 FmP F FmOP 381.195 503.499 M ( as empty)S -0.652 N (.)S FmE 58 72 468 116 rC 5793 0 :M FrMacBegin 58 72 468 115.333 FmKp B 0 FmP F FmOP 193.333 78.134 FmB 2.261 2.672 FmL 2 1 FmSo 195.594 80.806 FmB 83.478 98.656 FmL [6.802 6.802 ]6.802 F 2 1 FmDS 279.072 179.462 FmB 2.262 2.672 FmL 2 1 FmSo FmE 5793 0 :M ( )S 5795 0 :M FrMacBegin 58 72 468 115.333 FmKp B 0 FmP F FmOP FmG 268 156.037 M 0.96 0.96 scale ( s1)S FmR 282.667 78.134 FmB 2.234 2.694 FmL 2 1 FmSo 284.901 80.828 FmB 82.865 99.943 FmL [6.833 6.833 ]6.833 F 2 1 FmDS 367.765 180.772 FmB 2.235 2.696 FmL 2 1 FmSo FmG 352 156.467 M 0.96 0.96 scale (s2)S FmR 113.333 88.67 FmB 378 0 FmL 2 1 FmSo 113.333 124.67 FmB 378 0 FmL 2 1 FmSo 113.333 169.67 FmB 378 0 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 144.833 88.17 FmAF T 0 360 4.5 4.5 0 144.833 88.17 2 1 F FmAP 0 360 4.5 4.5 0 T 260.833 88.837 FmAF T 0 360 4.5 4.5 0 260.833 88.837 2 1 F FmAP 0 360 4.5 4.5 0 T 202.167 124.837 FmAF T 0 360 4.5 4.5 0 202.167 124.837 2 1 F FmAP 0 360 4.5 4.5 0 T 252.833 124.837 FmAF T 0 360 4.5 4.5 0 252.833 124.837 2 1 F FmAP 0 360 4.5 4.5 0 T 164.833 170.837 FmAF T 0 360 4.5 4.5 0 164.833 170.837 2 1 F FmAP 0 360 4.5 4.5 0 T 366.833 124.837 FmAF T 0 360 4.5 4.5 0 366.833 124.837 2 1 F FmAP 0 360 4.5 4.5 0 T 440.833 170.17 FmAF T 0 360 4.5 4.5 0 440.833 170.17 2 1 F FmAP 0 360 4.5 4.5 0 T 438.167 89.503 FmAF T 0 360 4.5 4.5 0 438.167 89.503 2 1 F FmAP FmE 5796 0 :M f289 sf ( )S 5799 0 :M FrMacBegin 58 72 468 115.333 FmKp B 0 FmP F FmOP 92.667 89.037 M (P)S FmE 5799 0 :M f148 sf ( )S 5801 0 :M FrMacBegin 58 72 468 115.333 FmKp B 0 FmP F FmOP FmG 99.997 92.037 M 0.96 0.96 scale (1)S FmR FmE 5801 0 :M f289 sf ( )S 5804 0 :M FrMacBegin 58 72 468 115.333 FmKp B 0 FmP F FmOP 92.667 126.371 M (P)S FmE 5804 0 :M f148 sf ( )S 5806 0 :M FrMacBegin 58 72 468 115.333 FmKp B 0 FmP F FmOP FmG 99.997 129.371 M 0.96 0.96 scale (2)S FmR FmE 5807 0 :M f289 sf ( )S 5810 0 :M FrMacBegin 58 72 468 115.333 FmKp B 0 FmP F FmOP 92.667 173.037 M (P)S FmE 5810 0 :M f148 sf ( )S 5812 0 :M FrMacBegin 58 72 468 115.333 FmKp B 0 FmP F FmOP FmG 99.997 176.037 M 0.96 0.96 scale (3)S FmR FmG 141.333 80.704 M 0.96 0.96 scale (e11)S FmR FmG 260.667 82.704 M 0.96 0.96 scale (e12)S FmR FmG 200 117.371 M 0.96 0.96 scale (e21)S FmR FmG 253.333 117.371 M 0.96 0.96 scale (e22)S FmR FmG 343.333 117.371 M 0.96 0.96 scale (e23)S FmR FmG 148.667 162.037 M 0.96 0.96 scale (e31)S FmR FmG 432 82.037 M 0.96 0.96 scale (e13)S FmR 329.026 115.998 FmB 1.257 -3.235 FmL 10.027 7.618 FmL -12.54 -1.147 FmL 1 FmS 329.026 115.998 FmB 1.257 -3.235 FmL 10.027 7.618 FmL -12.54 -1.147 FmL FmFl 261.333 89.704 FmB 67.227 26.113 FmL 2 1 FmSo 420.305 92.842 FmB -0.616 -3.416 FmL 12.529 1.266 FmL -11.296 5.565 FmL 1 FmS 420.305 92.842 FmB -0.616 -3.416 FmL 12.529 1.266 FmL -11.296 5.565 FmL FmFl 256.667 122.371 FmB 163.146 -29.44 FmL 2 1 FmSo 424.575 159.478 FmB 1.719 -3.015 FmL 8.798 9.01 FmL -12.235 -2.979 FmL 1 FmS 424.575 159.478 FmB 1.719 -3.015 FmL 8.798 9.01 FmL -12.235 -2.979 FmL FmFl 370 128.371 FmB 54.14 30.86 FmL 2 1 FmSo 191.653 138.309 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL 1 FmS 191.653 138.309 FmB -2.645 -2.248 FmL 10.484 -6.975 FmL -5.195 11.471 FmL FmFl 166.667 167.704 FmB 24.662 -29.014 FmL 2 1 FmSo 0 360 4.5 4.5 0 T 343.5 124.837 FmAF T 0 360 4.5 4.5 0 343.5 124.837 2 1 F FmAP 374.667 115.037 M (e24)S FmE endp showpage %%PageTrailer %%Page: 11 11 %%PageProcessColors: Black %%PageCustomColors: %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Matt Bishop; page: 11 of 11)setjob %%EndPageSetup gS 0 0 584 768 rC 5812 0 :M FrMacBegin 0 FmP F FmOP 0 FmSP FmE 58 33 468 14 rC 5812 0 :M FrMacBegin 58 34 468 12 FmKp B 0 FmP F FmOP 58 35 FmB 468 0 FmL 2 1 FmSo 58 38 FmB 468 0 FmL 2 1 FmSo FmE gR gS 0 0 584 768 rC 5812 0 :M f148 sf ( )S 5814 0 :M FrMacBegin B 0 FmP F FmOP 58 30.667 M (Huang\325s Termination Detection Protocol)S 22.398 N (ECS 251 \320 Winter 2001)S 154.015 N (Page )S (11)S 171.337 744 M (Last modified at )S (12:40 pm on Wednesday, January 31, 2001)S FmE 5815 0 :M f175 sf ( )S 5819 0 :M FrMacBegin B 0 FmP F FmOP 136.869 72 M (Huang\325)S -0.668 N (s )S -0.541 N (T)S -1.657 N (ermination Detection Pr)S -0.325 N (otocol)S FmE 5819 0 :M f263 sf ( )S 5822 0 :M FrMacBegin B 0 FmP F FmOP 58 104 M (Intr)S -0.217 N (oduction)S FmE 5822 0 :M f148 sf ( )S 5824 0 :M FrMacBegin B 0 FmP F FmOP 58 121.667 M (The goal of this protocol is to detect when a distrib)S -0.2 N (uted computation terminates.)S FmE 5825 0 :M f263 sf ( )S 5828 0 :M FrMacBegin B 0 FmP F FmOP 58 147 M (Notation)S FmE 5828 0 :M f148 sf ( )S 5830 0 :M FrMacBegin B 0 FmP F FmOP 58 164.667 M (\245)S FmE 5830 0 :M f203 sf ( )S 5832 0 :M FrMacBegin B 0 FmP F FmOP 76 164.667 M (n)S FmE 5833 0 :M f148 sf ( )S 5835 0 :M FrMacBegin B 0 FmP F FmOP 81 164.667 M ( processes)S 58 176.667 M (\245)S FmE 5835 0 :M f203 sf ( )S 5837 0 :M FrMacBegin B 0 FmP F FmOP 76 176.667 M (P)S FmE 5838 0 :M f250 sf ( )S 5840 0 :M FrMacBegin B 0 FmP F FmOP 82.108 179.167 M (i)S FmE 5840 0 :M f148 sf ( )S 5842 0 :M FrMacBegin B 0 FmP F FmOP 84.331 176.667 M ( process; without loss of generality)S -0.652 N (, let )S FmE 5842 0 :M f203 sf ( )S 5844 0 :M FrMacBegin B 0 FmP F FmOP 240.852 176.667 M (P)S FmE 5845 0 :M f276 sf ( )S 5847 0 :M FrMacBegin B 0 FmP F FmOP 246.96 179.167 M (0)S FmE 5847 0 :M f148 sf ( )S 5849 0 :M FrMacBegin B 0 FmP F FmOP 250.96 176.667 M ( be the )S FmE 5849 0 :M f203 sf ( )S 5851 0 :M FrMacBegin B 0 FmP F FmOP 280.116 176.667 M (contr)S -0.452 N (olling a)S -0.1 N (g)S -0.1 N (ent)S FmE 5852 0 :M f148 sf ( )S 5854 0 :M FrMacBegin B 0 FmP F FmOP 58 190.5 M (\245)S FmE 5854 0 :M f203 sf ( )S 5856 0 :M FrMacBegin B 0 FmP F FmOP 76 190.5 M (W)S FmE 5857 0 :M f250 sf ( )S 5859 0 :M FrMacBegin B 0 FmP F FmOP 83.886 193 M (i)S FmE 5859 0 :M f148 sf ( )S 5861 0 :M FrMacBegin B 0 FmP F FmOP 86.109 190.5 M (. weight of process )S FmE 5861 0 :M f203 sf ( )S 5863 0 :M FrMacBegin B 0 FmP F FmOP 164.134 190.5 M (P)S FmE 5864 0 :M f250 sf ( )S 5866 0 :M FrMacBegin B 0 FmP F FmOP 170.242 193 M (i)S FmE 5866 0 :M f148 sf ( )S 5868 0 :M FrMacBegin B 0 FmP F FmOP 172.465 190.5 M (; initially)S -0.652 N (, )S FmE 5868 0 :M f203 sf ( )S 5870 0 :M FrMacBegin B 0 FmP F FmOP 212.799 190.5 M (W)S FmE 5871 0 :M f276 sf ( )S 5873 0 :M FrMacBegin B 0 FmP F FmOP 221.127 193 M (0)S FmE 5873 0 :M f148 sf ( )S 5875 0 :M FrMacBegin B 0 FmP F FmOP 225.127 190.5 M ( = 1 and for all other )S FmE 5875 0 :M f203 sf ( )S 5877 0 :M FrMacBegin B 0 FmP F FmOP 309.9 190.5 M (i)S FmE 5878 0 :M f148 sf ( )S 5880 0 :M FrMacBegin B 0 FmP F FmOP 312.678 190.5 M (, )S FmE 5880 0 :M f203 sf ( )S 5882 0 :M FrMacBegin B 0 FmP F FmOP 317.278 190.5 M (W)S FmE 5883 0 :M f250 sf ( )S 5885 0 :M FrMacBegin B 0 FmP F FmOP 325.164 193 M (i)S FmE 5885 0 :M f148 sf ( )S 5887 0 :M FrMacBegin B 0 FmP F FmOP 327.387 190.5 M ( = 0.)S 58 204.333 M (\245)S FmE 5887 0 :M f203 sf ( )S 5889 0 :M FrMacBegin B 0 FmP F FmOP 76 204.333 M (B)S FmE 5890 0 :M f148 sf ( )S 5892 0 :M FrMacBegin B 0 FmP F FmOP 82.108 204.333 M (\()S FmE 5892 0 :M f203 sf ( )S 5894 0 :M FrMacBegin B 0 FmP F FmOP 85.436 204.333 M (W)S FmE 5895 0 :M f148 sf ( )S 5897 0 :M FrMacBegin B 0 FmP F FmOP 93.764 204.333 M (\) computation message with assigned weight )S FmE 5897 0 :M f203 sf ( )S 5899 0 :M FrMacBegin B 0 FmP F FmOP 274.977 204.333 M (W)S FmE 5900 0 :M f148 sf ( )S 5902 0 :M FrMacBegin B 0 FmP F FmOP 58 216.333 M (\245)S FmE 5902 0 :M f203 sf ( )S 5904 0 :M FrMacBegin B 0 FmP F FmOP 76 216.333 M (C)S FmE 5905 0 :M f148 sf ( )S 5907 0 :M FrMacBegin B 0 FmP F FmOP 82.67 216.333 M (\()S FmE 5907 0 :M f203 sf ( )S 5909 0 :M FrMacBegin B 0 FmP F FmOP 85.998 216.333 M (W)S FmE 5910 0 :M f148 sf ( )S 5912 0 :M FrMacBegin B 0 FmP F FmOP 94.325 216.333 M (\) control message sent from process to controlling agent with assigned weight )S FmE 5912 0 :M f203 sf ( )S 5914 0 :M FrMacBegin B 0 FmP F FmOP 407.707 216.333 M (W)S FmE 5915 0 :M f263 sf ( )S 5918 0 :M FrMacBegin B 0 FmP F FmOP 58 241.667 M (Pr)S -0.217 N (otocol)S FmE 5918 0 :M f319 sf ( )S 5920 0 :M FrMacBegin B 0 FmP F FmOP 58 259.333 M (P)S FmE 5920 0 :M f332 sf ( )S 5922 0 :M FrMacBegin B 0 FmP F FmOP 64.108 261.833 M (i)S FmE 5922 0 :M f345 sf ( )S 5924 0 :M FrMacBegin B 0 FmP F FmOP 66.331 259.333 M ( sends a computation message to )S FmE 5925 0 :M f319 sf ( )S 5927 0 :M FrMacBegin B 0 FmP F FmOP 206.854 259.333 M (P)S FmE 5927 0 :M f332 sf ( )S 5929 0 :M FrMacBegin B 0 FmP F FmOP 212.962 261.833 M (j)S FmE 5929 0 :M f148 sf ( )S 5931 0 :M FrMacBegin B 0 FmP F FmOP 58 273.166 M (1.)S 10.5 N (Set )S FmE 5932 0 :M f203 sf ( )S 5934 0 :M FrMacBegin B 0 FmP F FmOP 90.875 273.166 M (W)S FmE 5934 0 :M f250 sf ( )S 5936 0 :M FrMacBegin B 0 FmP F FmOP 98.762 275.666 M (i)S FmE 5936 0 :M f148 sf ( )S 5938 0 :M FrMacBegin B 0 FmP F FmOP 100.984 273.166 M (\325)S -0.742 N ( and )S FmE 5939 0 :M f203 sf ( )S 5941 0 :M FrMacBegin B 0 FmP F FmOP 122.608 273.166 M (W)S FmE 5941 0 :M f250 sf ( )S 5943 0 :M FrMacBegin B 0 FmP F FmOP 130.936 275.666 M (j)S FmE 5943 0 :M f148 sf ( )S 5945 0 :M FrMacBegin B 0 FmP F FmOP 133.158 273.166 M ( to v)S -0.251 N (alues such that )S FmE 5946 0 :M f203 sf ( )S 5948 0 :M FrMacBegin B 0 FmP F FmOP 211.652 273.166 M (W)S FmE 5948 0 :M f250 sf ( )S 5950 0 :M FrMacBegin B 0 FmP F FmOP 219.538 275.666 M (i)S FmE 5950 0 :M f148 sf ( )S 5952 0 :M FrMacBegin B 0 FmP F FmOP 221.761 273.166 M (\325)S -0.742 N ( + )S FmE 5953 0 :M f203 sf ( )S 5955 0 :M FrMacBegin B 0 FmP F FmOP 234.585 273.166 M (W)S FmE 5955 0 :M f250 sf ( )S 5957 0 :M FrMacBegin B 0 FmP F FmOP 242.913 275.666 M (j)S FmE 5957 0 :M f148 sf ( )S 5959 0 :M FrMacBegin B 0 FmP F FmOP 245.136 273.166 M ( = )S FmE 5960 0 :M f203 sf ( )S 5962 0 :M FrMacBegin B 0 FmP F FmOP 255.375 273.166 M (W)S FmE 5962 0 :M f250 sf ( )S 5964 0 :M FrMacBegin B 0 FmP F FmOP 263.261 275.666 M (i)S FmE 5964 0 :M f148 sf ( )S 5966 0 :M FrMacBegin B 0 FmP F FmOP 265.484 273.166 M (, )S FmE 5967 0 :M f203 sf ( )S 5969 0 :M FrMacBegin B 0 FmP F FmOP 270.084 273.166 M (W)S FmE 5969 0 :M f250 sf ( )S 5971 0 :M FrMacBegin B 0 FmP F FmOP 277.97 275.666 M (i)S FmE 5971 0 :M f148 sf ( )S 5973 0 :M FrMacBegin B 0 FmP F FmOP 280.192 273.166 M ( > 0, )S FmE 5974 0 :M f203 sf ( )S 5976 0 :M FrMacBegin B 0 FmP F FmOP 300.432 273.166 M (W)S FmE 5976 0 :M f250 sf ( )S 5978 0 :M FrMacBegin B 0 FmP F FmOP 308.759 275.666 M (j)S FmE 5978 0 :M f148 sf ( )S 5980 0 :M FrMacBegin B 0 FmP F FmOP 310.982 273.166 M ( > 0. \()S FmE 5981 0 :M f203 sf ( )S 5983 0 :M FrMacBegin B 0 FmP F FmOP 334.949 273.166 M (W)S FmE 5983 0 :M f250 sf ( )S 5985 0 :M FrMacBegin B 0 FmP F FmOP 342.836 275.666 M (i)S FmE 5985 0 :M f148 sf ( )S 5987 0 :M FrMacBegin B 0 FmP F FmOP 345.058 273.166 M (\325)S -0.742 N ( is the ne)S -0.251 N (w weight of )S FmE 5988 0 :M f203 sf ( )S 5990 0 :M FrMacBegin B 0 FmP F FmOP 433.476 273.166 M (P)S FmE 5990 0 :M f250 sf ( )S 5992 0 :M FrMacBegin B 0 FmP F FmOP 439.585 275.666 M (i)S FmE 5992 0 :M f148 sf ( )S 5994 0 :M FrMacBegin B 0 FmP F FmOP 441.807 273.166 M (.\))S 58 287.3 M (2.)S 10.5 N (Send )S FmE 5995 0 :M f203 sf ( )S 5997 0 :M FrMacBegin B 0 FmP F FmOP 98.498 287.3 M (B)S FmE 5997 0 :M f148 sf ( )S 5999 0 :M FrMacBegin B 0 FmP F FmOP 104.606 287.3 M (\()S FmE 6000 0 :M f203 sf ( )S 6002 0 :M FrMacBegin B 0 FmP F FmOP 107.934 287.3 M (W)S FmE 6002 0 :M f250 sf ( )S 6004 0 :M FrMacBegin B 0 FmP F FmOP 116.261 289.8 M (j)S FmE 6004 0 :M f148 sf ( )S 6006 0 :M FrMacBegin B 0 FmP F FmOP 118.484 287.3 M (\) to )S FmE 6007 0 :M f203 sf ( )S 6009 0 :M FrMacBegin B 0 FmP F FmOP 134.59 287.3 M (P)S FmE 6009 0 :M f250 sf ( )S 6011 0 :M FrMacBegin B 0 FmP F FmOP 140.698 289.8 M (j)S FmE 6011 0 :M f319 sf ( )S 6013 0 :M FrMacBegin B 0 FmP F FmOP 58 301.433 M (P)S FmE 6014 0 :M f332 sf ( )S 6016 0 :M FrMacBegin B 0 FmP F FmOP 64.108 303.933 M (j)S FmE 6016 0 :M f345 sf ( )S 6018 0 :M FrMacBegin B 0 FmP F FmOP 66.331 301.433 M ( r)S -0.181 N (ecei)S -0.1 N (v)S -0.1 N (es a computation message )S FmE 6018 0 :M f319 sf ( )S 6020 0 :M FrMacBegin B 0 FmP F FmOP 206.17 301.433 M (B)S FmE 6021 0 :M f345 sf ( )S 6023 0 :M FrMacBegin B 0 FmP F FmOP 212.84 301.433 M (\()S FmE 6023 0 :M f319 sf ( )S 6025 0 :M FrMacBegin B 0 FmP F FmOP 216.167 301.433 M (W)S FmE 6026 0 :M f345 sf ( )S 6028 0 :M FrMacBegin B 0 FmP F FmOP 225.057 301.433 M (\) fr)S -0.181 N (om )S FmE 6028 0 :M f319 sf ( )S 6030 0 :M FrMacBegin B 0 FmP F FmOP 254.297 301.433 M (P)S FmE 6031 0 :M f332 sf ( )S 6033 0 :M FrMacBegin B 0 FmP F FmOP 260.406 303.933 M (i)S FmE 6033 0 :M f148 sf ( )S 6035 0 :M FrMacBegin B 0 FmP F FmOP 58 315.266 M (1.)S FmE 6035 0 :M f203 sf ( )S 6037 0 :M FrMacBegin B 0 FmP F FmOP 76 315.266 M (W)S FmE 6038 0 :M f250 sf ( )S 6040 0 :M FrMacBegin B 0 FmP F FmOP 84.328 317.766 M (j)S FmE 6040 0 :M f148 sf ( )S 6042 0 :M FrMacBegin B 0 FmP F FmOP 86.55 315.266 M ( = )S FmE 6042 0 :M f203 sf ( )S 6044 0 :M FrMacBegin B 0 FmP F FmOP 96.79 315.266 M (W)S FmE 6045 0 :M f250 sf ( )S 6047 0 :M FrMacBegin B 0 FmP F FmOP 105.117 317.766 M (j)S FmE 6047 0 :M f148 sf ( )S 6049 0 :M FrMacBegin B 0 FmP F FmOP 107.34 315.266 M ( + )S FmE 6049 0 :M f203 sf ( )S 6051 0 :M FrMacBegin B 0 FmP F FmOP 117.579 315.266 M (W)S FmE 6052 0 :M f148 sf ( )S 6054 0 :M FrMacBegin B 0 FmP F FmOP 58 329.4 M (2.)S 10.5 N (If )S FmE 6054 0 :M f203 sf ( )S 6056 0 :M FrMacBegin B 0 FmP F FmOP 85.155 329.4 M (P)S FmE 6057 0 :M f250 sf ( )S 6059 0 :M FrMacBegin B 0 FmP F FmOP 91.264 331.9 M (j)S FmE 6059 0 :M f148 sf ( )S 6061 0 :M FrMacBegin B 0 FmP F FmOP 93.486 329.4 M ( is idle, )S FmE 6061 0 :M f203 sf ( )S 6063 0 :M FrMacBegin B 0 FmP F FmOP 125.149 329.4 M (P)S FmE 6064 0 :M f250 sf ( )S 6066 0 :M FrMacBegin B 0 FmP F FmOP 131.257 331.9 M (j)S FmE 6066 0 :M f148 sf ( )S 6068 0 :M FrMacBegin B 0 FmP F FmOP 133.48 329.4 M ( becomes acti)S -0.251 N (v)S -0.151 N (e)S FmE 6068 0 :M f319 sf ( )S 6070 0 :M FrMacBegin B 0 FmP F FmOP 58 343.533 M (P)S FmE 6071 0 :M f332 sf ( )S 6073 0 :M FrMacBegin B 0 FmP F FmOP 64.108 346.033 M (i)S FmE 6073 0 :M f345 sf ( )S 6075 0 :M FrMacBegin B 0 FmP F FmOP 66.331 343.533 M ( becomes idle:)S FmE 6075 0 :M f148 sf ( )S 6077 0 :M FrMacBegin B 0 FmP F FmOP 58 357.366 M (1.)S 10.5 N (Send )S FmE 6078 0 :M f203 sf ( )S 6080 0 :M FrMacBegin B 0 FmP F FmOP 98.498 357.366 M (C)S FmE 6080 0 :M f148 sf ( )S 6082 0 :M FrMacBegin B 0 FmP F FmOP 105.167 357.366 M (\()S FmE 6083 0 :M f203 sf ( )S 6085 0 :M FrMacBegin B 0 FmP F FmOP 108.495 357.366 M (W)S FmE 6085 0 :M f250 sf ( )S 6087 0 :M FrMacBegin B 0 FmP F FmOP 116.381 359.866 M (i)S FmE 6087 0 :M f148 sf ( )S 6089 0 :M FrMacBegin B 0 FmP F FmOP 118.604 357.366 M (\) to )S FmE 6090 0 :M f203 sf ( )S 6092 0 :M FrMacBegin B 0 FmP F FmOP 134.71 357.366 M (P)S FmE 6092 0 :M f276 sf ( )S 6094 0 :M FrMacBegin B 0 FmP F FmOP 140.818 359.866 M (0)S FmE 6094 0 :M f148 sf ( )S 6096 0 :M FrMacBegin B 0 FmP F FmOP 58 371.499 M (2.)S FmE 6097 0 :M f203 sf ( )S 6099 0 :M FrMacBegin B 0 FmP F FmOP 76 371.499 M (W)S FmE 6099 0 :M f250 sf ( )S 6101 0 :M FrMacBegin B 0 FmP F FmOP 83.886 373.999 M (i)S FmE 6101 0 :M f148 sf ( )S 6103 0 :M FrMacBegin B 0 FmP F FmOP 86.109 371.499 M ( = 0)S 58 385.633 M (3.)S FmE 6104 0 :M f203 sf ( )S 6106 0 :M FrMacBegin B 0 FmP F FmOP 76 385.633 M (P)S FmE 6106 0 :M f250 sf ( )S 6108 0 :M FrMacBegin B 0 FmP F FmOP 82.108 388.133 M (i)S FmE 6108 0 :M f148 sf ( )S 6110 0 :M FrMacBegin B 0 FmP F FmOP 84.331 385.633 M ( becomes idle)S FmE 6111 0 :M f319 sf ( )S 6113 0 :M FrMacBegin B 0 FmP F FmOP 58 399.766 M (P)S FmE 6113 0 :M f332 sf ( )S 6115 0 :M FrMacBegin B 0 FmP F FmOP 64.108 402.266 M (i)S FmE 6115 0 :M f345 sf ( )S 6117 0 :M FrMacBegin B 0 FmP F FmOP 66.331 399.766 M ( r)S -0.181 N (ecei)S -0.1 N (v)S -0.1 N (es a contr)S -0.181 N (ol message )S FmE 6118 0 :M f319 sf ( )S 6120 0 :M FrMacBegin B 0 FmP F FmOP 182.654 399.766 M (C)S FmE 6120 0 :M f345 sf ( )S 6122 0 :M FrMacBegin B 0 FmP F FmOP 189.324 399.766 M (\()S FmE 6123 0 :M f319 sf ( )S 6125 0 :M FrMacBegin B 0 FmP F FmOP 192.652 399.766 M (W)S FmE 6125 0 :M f345 sf ( )S 6127 0 :M FrMacBegin B 0 FmP F FmOP 201.541 399.766 M (\):)S FmE 6128 0 :M f148 sf ( )S 6130 0 :M FrMacBegin B 0 FmP F FmOP 58 413.599 M (1.)S FmE 6130 0 :M f203 sf ( )S 6132 0 :M FrMacBegin B 0 FmP F FmOP 76 413.599 M (W)S FmE 6133 0 :M f250 sf ( )S 6135 0 :M FrMacBegin B 0 FmP F FmOP 83.886 416.099 M (i)S FmE 6135 0 :M f148 sf ( )S 6137 0 :M FrMacBegin B 0 FmP F FmOP 86.109 413.599 M ( = )S FmE 6137 0 :M f203 sf ( )S 6139 0 :M FrMacBegin B 0 FmP F FmOP 96.348 413.599 M (W)S FmE 6140 0 :M f250 sf ( )S 6142 0 :M FrMacBegin B 0 FmP F FmOP 104.234 416.099 M (i)S FmE 6142 0 :M f148 sf ( )S 6144 0 :M FrMacBegin B 0 FmP F FmOP 106.457 413.599 M ( + )S FmE 6144 0 :M f203 sf ( )S 6146 0 :M FrMacBegin B 0 FmP F FmOP 116.696 413.599 M (W)S FmE 6147 0 :M f148 sf ( )S 6149 0 :M FrMacBegin B 0 FmP F FmOP 58 427.732 M (2.)S 10.5 N (If )S FmE 6149 0 :M f203 sf ( )S 6151 0 :M FrMacBegin B 0 FmP F FmOP 84.755 427.732 M (W)S FmE 6152 0 :M f250 sf ( )S 6154 0 :M FrMacBegin B 0 FmP F FmOP 92.641 430.232 M (i)S FmE 6154 0 :M f148 sf ( )S 6156 0 :M FrMacBegin B 0 FmP F FmOP 94.864 427.732 M ( = 1, the computation has completed.)S FmE 6156 0 :M f263 sf ( )S 6159 0 :M FrMacBegin B 0 FmP F FmOP 58 454.899 M (Example)S FmE 6159 0 :M f148 sf ( )S 6161 0 :M FrMacBegin B 0 FmP F FmOP 233.992 472.566 M (The picture sho)S -0.251 N (ws a process )S FmE 6162 0 :M f203 sf ( )S 6164 0 :M FrMacBegin B 0 FmP F FmOP 348.968 472.566 M (P)S FmE 6164 0 :M f276 sf ( )S 6166 0 :M FrMacBegin B 0 FmP F FmOP 355.076 475.066 M (0)S FmE 6166 0 :M f148 sf ( )S 6168 0 :M FrMacBegin B 0 FmP F FmOP 359.076 472.566 M (, designated the )S FmE 6169 0 :M f203 sf ( )S 6171 0 :M FrMacBegin B 0 FmP F FmOP 424.054 472.566 M (contr)S -0.452 N (olling a)S -0.1 N (g)S -0.1 N (ent)S FmE 6171 0 :M f148 sf ( )S 6173 0 :M FrMacBegin B 0 FmP F FmOP 492.56 472.566 M (, with )S FmE 6174 0 :M f203 sf ( )S 6176 0 :M FrMacBegin B 0 FmP F FmOP 233.992 486.399 M (W)S FmE 6176 0 :M f276 sf ( )S 6178 0 :M FrMacBegin B 0 FmP F FmOP 242.32 488.899 M (0)S FmE 6178 0 :M f148 sf ( )S 6180 0 :M FrMacBegin B 0 FmP F FmOP 246.32 486.399 M -0.307( = 1. It asks )W FmE 6181 0 :M f203 sf ( )S 6183 0 :M FrMacBegin B 0 FmP F FmOP 293.749 486.399 M (P)S FmE 6183 0 :M f276 sf ( )S 6185 0 :M FrMacBegin B 0 FmP F FmOP 299.858 488.899 M (1)S FmE 6185 0 :M f148 sf ( )S 6187 0 :M FrMacBegin B 0 FmP F FmOP 303.858 486.399 M -0.307( and )W FmE 6188 0 :M f203 sf ( )S 6190 0 :M FrMacBegin B 0 FmP F FmOP 322.683 486.399 M (P)S FmE 6190 0 :M f276 sf ( )S 6192 0 :M FrMacBegin B 0 FmP F FmOP 328.791 488.899 M (2)S FmE 6192 0 :M f148 sf ( )S 6194 0 :M FrMacBegin B 0 FmP F FmOP 332.791 486.399 M -0.307( to do some computation.)W -0.307( It sets )W FmE 6195 0 :M f203 sf ( )S 6197 0 :M FrMacBegin B 0 FmP F FmOP 460.221 486.399 M (W)S FmE 6197 0 :M f276 sf ( )S 6199 0 :M FrMacBegin B 0 FmP F FmOP 468.548 488.899 M (1)S FmE 6199 0 :M f148 sf ( )S 6201 0 :M FrMacBegin B 0 FmP F FmOP 472.548 486.399 M -0.307( to 0.2, )W FmE 6202 0 :M f203 sf ( )S 6204 0 :M FrMacBegin B 0 FmP F FmOP 501.507 486.399 M (W)S FmE 6204 0 :M f276 sf ( )S 6206 0 :M FrMacBegin B 0 FmP F FmOP 509.834 488.899 M (2)S FmE 6206 0 :M f148 sf ( )S 6208 0 :M FrMacBegin B 0 FmP F FmOP 513.834 486.399 M -0.307( to )W 233.992 500.232 M -0.11(0.3, and )W FmE 6209 0 :M f203 sf ( )S 6211 0 :M FrMacBegin B 0 FmP F FmOP 267.81 500.232 M (W)S FmE 6211 0 :M f276 sf ( )S 6213 0 :M FrMacBegin B 0 FmP F FmOP 276.138 502.732 M (3)S FmE 6213 0 :M f148 sf ( )S 6215 0 :M FrMacBegin B 0 FmP F FmOP 280.138 500.232 M -0.11( to 0.5. )W FmE 6216 0 :M f203 sf ( )S 6218 0 :M FrMacBegin B 0 FmP F FmOP 310.086 500.232 M (P)S FmE 6218 0 :M f276 sf ( )S 6220 0 :M FrMacBegin B 0 FmP F FmOP 316.194 502.732 M (2)S FmE 6220 0 :M f148 sf ( )S 6222 0 :M FrMacBegin B 0 FmP F FmOP 320.194 500.232 M -0.11( in turn asks )W FmE 6223 0 :M f203 sf ( )S 6225 0 :M FrMacBegin B 0 FmP F FmOP 370.855 500.232 M (P)S FmE 6225 0 :M f276 sf ( )S 6227 0 :M FrMacBegin B 0 FmP F FmOP 376.963 502.732 M (3)S FmE 6227 0 :M f148 sf ( )S 6229 0 :M FrMacBegin B 0 FmP F FmOP 380.963 500.232 M -0.11( and )W FmE 6230 0 :M f203 sf ( )S 6232 0 :M FrMacBegin B 0 FmP F FmOP 400.182 500.232 M (P)S FmE 6232 0 :M f276 sf ( )S 6234 0 :M FrMacBegin B 0 FmP F FmOP 406.29 502.732 M (4)S FmE 6234 0 :M f148 sf ( )S 6236 0 :M FrMacBegin B 0 FmP F FmOP 410.29 500.232 M -0.11( to do some computations. It )W 233.992 514.066 M (sets )S FmE 6237 0 :M f203 sf ( )S 6239 0 :M FrMacBegin B 0 FmP F FmOP 251.087 514.066 M (W)S FmE 6239 0 :M f276 sf ( )S 6241 0 :M FrMacBegin B 0 FmP F FmOP 259.414 516.566 M (3)S FmE 6241 0 :M f148 sf ( )S 6243 0 :M FrMacBegin B 0 FmP F FmOP 263.414 514.066 M ( to 0.1 and )S FmE 6244 0 :M f203 sf ( )S 6246 0 :M FrMacBegin B 0 FmP F FmOP 307.731 514.066 M (W)S FmE 6246 0 :M f276 sf ( )S 6248 0 :M FrMacBegin B 0 FmP F FmOP 316.058 516.566 M (4)S FmE 6248 0 :M f148 sf ( )S 6250 0 :M FrMacBegin B 0 FmP F FmOP 320.058 514.066 M ( to 0.1.)S 233.992 527.899 M -0.196(When )W FmE 6251 0 :M f203 sf ( )S 6253 0 :M FrMacBegin B 0 FmP F FmOP 260.173 527.899 M (P)S FmE 6253 0 :M f276 sf ( )S 6255 0 :M FrMacBegin B 0 FmP F FmOP 266.281 530.399 M (3)S FmE 6255 0 :M f148 sf ( )S 6257 0 :M FrMacBegin B 0 FmP F FmOP 270.281 527.899 M -0.196( terminates, it sends C\()W FmE 6258 0 :M f203 sf ( )S 6260 0 :M FrMacBegin B 0 FmP F FmOP 361.413 527.899 M (W)S FmE 6260 0 :M f276 sf ( )S 6262 0 :M FrMacBegin B 0 FmP F FmOP 369.74 530.399 M (3)S FmE 6262 0 :M f148 sf ( )S 6264 0 :M FrMacBegin B 0 FmP F FmOP 373.74 527.899 M -0.196(\) = C\(0.1\) to )W FmE 6265 0 :M f203 sf ( )S 6267 0 :M FrMacBegin B 0 FmP F FmOP 425.526 527.899 M (P)S FmE 6267 0 :M f276 sf ( )S 6269 0 :M FrMacBegin B 0 FmP F FmOP 431.635 530.399 M (2)S FmE 6269 0 :M f148 sf ( )S 6271 0 :M FrMacBegin B 0 FmP F FmOP 435.635 527.899 M -0.196(, which changes )W FmE 6272 0 :M f203 sf ( )S 6274 0 :M FrMacBegin B 0 FmP F FmOP 501.286 527.899 M (W)S FmE 6274 0 :M f276 sf ( )S 6276 0 :M FrMacBegin B 0 FmP F FmOP 509.614 530.399 M (2)S FmE 6276 0 :M f148 sf ( )S 6278 0 :M FrMacBegin B 0 FmP F FmOP 513.614 527.899 M -0.196( to )W 233.992 541.732 M (0.1 + 0.1 = 0.2.)S 233.992 553.732 M -0.196(When )W FmE 6279 0 :M f203 sf ( )S 6281 0 :M FrMacBegin B 0 FmP F FmOP 260.173 553.732 M (P)S FmE 6281 0 :M f276 sf ( )S 6283 0 :M FrMacBegin B 0 FmP F FmOP 266.281 556.232 M (2)S FmE 6283 0 :M f148 sf ( )S 6285 0 :M FrMacBegin B 0 FmP F FmOP 270.281 553.732 M -0.196( terminates, it sends C\()W FmE 6286 0 :M f203 sf ( )S 6288 0 :M FrMacBegin B 0 FmP F FmOP 361.413 553.732 M (W)S FmE 6288 0 :M f276 sf ( )S 6290 0 :M FrMacBegin B 0 FmP F FmOP 369.74 556.232 M (2)S FmE 6290 0 :M f148 sf ( )S 6292 0 :M FrMacBegin B 0 FmP F FmOP 373.74 553.732 M -0.196(\) = C\(0.2\) to )W FmE 6293 0 :M f203 sf ( )S 6295 0 :M FrMacBegin B 0 FmP F FmOP 425.526 553.732 M (P)S FmE 6295 0 :M f276 sf ( )S 6297 0 :M FrMacBegin B 0 FmP F FmOP 431.635 556.232 M (0)S FmE 6297 0 :M f148 sf ( )S 6299 0 :M FrMacBegin B 0 FmP F FmOP 435.635 553.732 M -0.196(, which changes )W FmE 6300 0 :M f203 sf ( )S 6302 0 :M FrMacBegin B 0 FmP F FmOP 501.286 553.732 M (W)S FmE 6302 0 :M f276 sf ( )S 6304 0 :M FrMacBegin B 0 FmP F FmOP 509.614 556.232 M (0)S FmE 6304 0 :M f148 sf ( )S 6306 0 :M FrMacBegin B 0 FmP F FmOP 513.614 553.732 M -0.196( to )W 233.992 567.565 M (0.5 + 0.2 = 0.7.)S 233.992 579.565 M -0.196(When )W FmE 6307 0 :M f203 sf ( )S 6309 0 :M FrMacBegin B 0 FmP F FmOP 260.173 579.565 M (P)S FmE 6309 0 :M f276 sf ( )S 6311 0 :M FrMacBegin B 0 FmP F FmOP 266.281 582.065 M (4)S FmE 6311 0 :M f148 sf ( )S 6313 0 :M FrMacBegin B 0 FmP F FmOP 270.281 579.565 M -0.196( terminates, it sends C\()W FmE 6314 0 :M f203 sf ( )S 6316 0 :M FrMacBegin B 0 FmP F FmOP 361.413 579.565 M (W)S FmE 6316 0 :M f276 sf ( )S 6318 0 :M FrMacBegin B 0 FmP F FmOP 369.74 582.065 M (4)S FmE 6318 0 :M f148 sf ( )S 6320 0 :M FrMacBegin B 0 FmP F FmOP 373.74 579.565 M -0.196(\) = C\(0.1\) to )W FmE 6321 0 :M f203 sf ( )S 6323 0 :M FrMacBegin B 0 FmP F FmOP 425.526 579.565 M (P)S FmE 6323 0 :M f276 sf ( )S 6325 0 :M FrMacBegin B 0 FmP F FmOP 431.635 582.065 M (0)S FmE 6325 0 :M f148 sf ( )S 6327 0 :M FrMacBegin B 0 FmP F FmOP 435.635 579.565 M -0.196(, which changes )W FmE 6328 0 :M f203 sf ( )S 6330 0 :M FrMacBegin B 0 FmP F FmOP 501.286 579.565 M (W)S FmE 6330 0 :M f276 sf ( )S 6332 0 :M FrMacBegin B 0 FmP F FmOP 509.614 582.065 M (0)S FmE 6332 0 :M f148 sf ( )S 6334 0 :M FrMacBegin B 0 FmP F FmOP 513.614 579.565 M -0.196( to )W 233.992 593.399 M (0.7 + 0.1 = 0.8.)S 233.992 605.399 M -0.196(When )W FmE 6335 0 :M f203 sf ( )S 6337 0 :M FrMacBegin B 0 FmP F FmOP 260.173 605.399 M (P)S FmE 6337 0 :M f276 sf ( )S 6339 0 :M FrMacBegin B 0 FmP F FmOP 266.281 607.899 M (1)S FmE 6339 0 :M f148 sf ( )S 6341 0 :M FrMacBegin B 0 FmP F FmOP 270.281 605.399 M -0.196( terminates, it sends C\()W FmE 6342 0 :M f203 sf ( )S 6344 0 :M FrMacBegin B 0 FmP F FmOP 361.413 605.399 M (W)S FmE 6344 0 :M f276 sf ( )S 6346 0 :M FrMacBegin B 0 FmP F FmOP 369.74 607.899 M (1)S FmE 6346 0 :M f148 sf ( )S 6348 0 :M FrMacBegin B 0 FmP F FmOP 373.74 605.399 M -0.196(\) = C\(0.2\) to )W FmE 6349 0 :M f203 sf ( )S 6351 0 :M FrMacBegin B 0 FmP F FmOP 425.526 605.399 M (P)S FmE 6351 0 :M f276 sf ( )S 6353 0 :M FrMacBegin B 0 FmP F FmOP 431.635 607.899 M (0)S FmE 6353 0 :M f148 sf ( )S 6355 0 :M FrMacBegin B 0 FmP F FmOP 435.635 605.399 M -0.196(, which changes )W FmE 6356 0 :M f203 sf ( )S 6358 0 :M FrMacBegin B 0 FmP F FmOP 501.286 605.399 M (W)S FmE 6358 0 :M f276 sf ( )S 6360 0 :M FrMacBegin B 0 FmP F FmOP 509.614 607.899 M (0)S FmE 6360 0 :M f148 sf ( )S 6362 0 :M FrMacBegin B 0 FmP F FmOP 513.614 605.399 M -0.196( to )W 233.992 619.232 M (0.8 + 0.2 = 1.)S FmE 6363 0 :M f203 sf ( )S 6365 0 :M FrMacBegin B 0 FmP F FmOP 58 631.232 M (P)S FmE 6365 0 :M f276 sf ( )S 6367 0 :M FrMacBegin B 0 FmP F FmOP 64.108 633.732 M (0)S FmE 6367 0 :M f148 sf ( )S 6369 0 :M FrMacBegin B 0 FmP F FmOP 68.108 631.232 M ( thereupon concludes that the computation is \336)S (nished.)S 58 645.065 M (T)S -0.801 N (otal number of messages passed: 8 \(one to start each computation, one to return the weight\).)S FmE 58 465 170 145 rC 6370 0 :M FrMacBegin 58 465.899 169.992 144 FmKp B 0 FmP F FmOP 0 360 5 4.667 0 T 75.667 516.333 FmAF T 0 360 5 4.667 0 75.667 516.333 2 1 [7.401 7.401 ]0 T FmAP 0 360 5 4.667 0 T 127 489 FmAF T 0 360 5 4.667 0 127 489 2 1 [7.401 7.401 ]0 T FmAP 0 360 5 4.667 0 T 125 544.333 FmAF T 0 360 5 4.667 0 125 544.333 2 1 [7.401 7.401 ]0 T FmAP 0 360 5 4.667 0 T 175.667 519 FmAF T 0 360 5 4.667 0 175.667 519 2 1 [7.401 7.401 ]0 T FmAP 0 360 5 4.667 0 T 174.333 570.333 FmAF T 0 360 5 4.667 0 174.333 570.333 2 1 [7.401 7.401 ]0 T FmAP 109.667 534.882 FmB 1.609 -3.076 FmL 9.117 8.686 FmL -12.335 -2.535 FmL 1 FmS 109.667 534.882 FmB 1.609 -3.076 FmL 9.117 8.686 FmL -12.335 -2.535 FmL FmFl 78.667 518.667 FmB 30.557 15.984 FmL 2 1 FmSo 159 560.882 FmB 1.609 -3.076 FmL 9.117 8.686 FmL -12.335 -2.535 FmL 1 FmS 159 560.882 FmB 1.609 -3.076 FmL 9.117 8.686 FmL -12.335 -2.535 FmL FmFl 128 544.667 FmB 30.557 15.984 FmL 2 1 FmSo 111.478 497.41 FmB -1.515 -3.123 FmL 12.406 -2.162 FmL -9.375 8.408 FmL 1 FmS 111.478 497.41 FmB -1.515 -3.123 FmL 12.406 -2.162 FmL -9.375 8.408 FmL FmFl 78.667 513.333 FmB 32.362 -15.705 FmL 2 1 FmSo 159.551 525.558 FmB -1.552 -3.105 FmL 12.379 -2.309 FmL -9.275 8.518 FmL 1 FmS 159.551 525.558 FmB -1.552 -3.105 FmL 12.379 -2.309 FmL -9.275 8.518 FmL FmFl 129.333 540.667 FmB 29.77 -14.885 FmL 2 1 FmSo FmE 6370 0 :M ( )S 6372 0 :M FrMacBegin 58 465.899 169.992 144 FmKp B 0 FmP F FmOP 62.667 530 M (P0)S 132.667 477.333 M (P1)S 121.333 527.333 M (P2)S 174 508.667 M (P3)S 174 556.667 M (P4)S FmE endp showpage %%PageTrailer %%Trailer end %%EOF