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Table All7Table<$paranumonly>, <$paratext>, on page<$pagenum>Table Number & Page'Table<$paranumonly> on page<$pagenum> Handout DateJanuary 7, 1999Heading <$paratext>AHHTMLHeadingsA;;==??Ac5y??? 5 5*C3.Ba.?*???"?$?& ?( ?* ?, ?. ?0 ?2 ?4 ?6 ?8 ?: ?< ?> ?@ ?B ?D ?F ?H ?J ?L ?N ?P ?R ?T ?V Cb.>+C2.?X ?Z ?\ ?^ ?` ?b E E ?f ?h ?j ?l ?n ?p ?r ?t ?v ?x E E ?| ?~ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? E E ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? FH FJ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? F| F~ ? ? ? @ @ @ @ @ @  @  @ @ @ @ @ @ @ @ @ @  @" @$ ABADAFAH AJ AL AN APAR AT@& @( @* @, @. @0 @2 @4 @6 @8 @: @< @> @@ @B @D @F @H @J @L @N @P @R @T @V @X @Z @\ @^ @` @b @d @f @h @j @l @n @p @r @t @v @x @z @| Ca.@~ @ @ @@D' >1.C4.@@ @ @ @ AVAX AZ@ @ @ @ @ A\A^ @ @ @ @ @ @ @ @ @ @@@@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ rAe@ @ @ @ @ @ @ @ @ @ @ @ GP GR G] @@@@ @ @ @ A A DD D A AAAA A A A A A A  A" A%A'A)A+ A- A/ A1 A3 A5 A6Ca.Cc.Cd.Ce.Cb.Ca.Cc.D) D+ D- D/ D1 D3 Cb.D5 D7 D9 D; D= D? DA DC DE DG DI D D D D D D D G_ Ga Gc Ge Gg Gi Gk Gm Go Gq Gs Gu Gw Gy G{ G} G G G G G G G G G G H  H  H H H H rdq}? D&G5I? IFWRe d? HmR? HmRHRHRFootnote Hr@? Hr@HzHz Single LineH? Footnote ?   HD?  HDHH Double LineH? Double Line? ? H?  Single Line? HZ?  TableFootnote EGxR?EGxREPwEPw TableFootnoted5p HHˆ5xHHˆGe HHˆ5zHHˆld?d?dHl d?d%i%`[^adgjmprovy| #'+/ADOL963W3Bm       }d ?!d WeHTML Mapping Table }Hd ?Hd We }Hd ?Hd We HUV 5HUV Ge HUV 5HUV l H$ 5H$ Ge H$ 5H$ l HHˆ5HHˆ( `Outline for April 11, 2000 S`Greetings and felicitations! ` Homework '` Handouts )P`vGeneral case: It is undecidable whether a given state of a given protection system is safe for a given generic right. L\`2Represent TM as ACM; reduce halting problem to it j` Take-Grant 4v`(Introduce as counterpoint to HRU result 8`>Show bridges (as a combination of terminal and initial spans) 5`;Show islands (maximal subject-only tg-connected subgraphs) !6 Bcanshare( r ,  x ,  y , G 0 ) iff there is an edge from  x  to  y  labelled  r  in G 0 , or all of the following hold: (1) there /is a vertex   y  with an edge from  y  to  y  labelled  r ; (2) there is a subject  y  which terminally spans to  y , or *y  =  y ; (3) there is a subject  x  which initially spans to  x , or  x  =  x ; and (4) there is a sequence of islands #@I 1 , ...,  I n  connected by bridges for which  x  is in  I 1  and  y  is in  I n  . 7`(Describe cansteal; dont state theorem Tت` Decidability vs. Undecidability 9䪛`&Notion of type; subject, object types A` Attenuation: A:`_If attenuating acyclic, its decidable; so that is sufficient. Open question: is it necessary? 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