- Greetings and felicitations!
- Please get your project proposals in as soon as possible, so you can get started
- Hand out new homework; point out #6 and review rules of attacking
*lassen*over the network

- Take-Grant
- Show bridges (as a combination of terminal and initial spans)
- Show islands (maximal subject-only tg-connected subgraphs)
- can*share(
*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*connected by bridges for which_{n}**x'**is in*I*_{1}and**y'**is in*I*._{n} - Describe can*steal; don't state theorem

- Decidability vs. Undecidability
- Notion of type; subject, object types
- SPM: types fixed at creation
- tickets:
**X**/*r*(apply right*r*to entity**X**),**X**/*r*:*c*(*c*copy flag, so can give right away) - link predicate:
**X**possesses tickets in set*dom*(**X**). Then*link*(**X**,**Y**) = rights over**X**and**Y***dom*(**X**) and*dom*(**Y**), and true; basically, everything connecting**X**and**Y** - copying
**X**/*r*:*c*from*dom*(**X**) to*dom*(**Z**): needs**X**/*rc**dom*(**X**), link(**X**,**Z**), and [[tau]](**X**)/*r*:*c**f*([[tau]](**X**), [[tau]](**Z**)),*f*filter function - Do TG example pp. 82-83
- create: can-create (
*cc*) relation says that subject of type*a*can create entities of type*b*iff*cc*(*a*,*b*) holds - create rule:
*cr*(_{p}*a*,*b*) = set of tickets added to*dom*(A),*cr*(_{c}*a*,*b*) = set of tickets added to*dom*(B) - attenuation:
*cr*(*a*,*b*) =*cr*p(_{p}*a*,*b*)|*cr*(_{c}*a*,*b*) is attenuating if: (1)*cr*(_{c}*a*,*b*) SUBSETEQ*cr*_{p}(*a*,*b*) and (2)*a*/*r*:*c*SUBSETEQ*cr*(_{p}*a*,*b*)*self*/*r*:*c**cr*(_{p}*a*,*b*) - cyclic:
*cc*(*a*,*b*)*cc*(*b*,*a*) - if attenuating acyclic, it's decidable; so that is sufficient. Open question: is it necessary?

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Department of Computer Science

University of California at Davis

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