Volume III: Progress

# Temporal Verification of Reactive Systems: Safety

• Notes
• davidvictor
• 12

This preview shows pages 1–4. Sign up to view the full content.

CS256/Winter 2007 — Lecture #16 Zohar Manna Announcements: Last homework will be assigned on Thursday. References for further reading: Volume III of Manna & Pnueli, Chapter 1 Zohar Manna and Amir Pnueli. “Completing the Temporal Picture.” In Theoretical Computer Science Journal , 83(1), 1991, pp. 97–130. References are available from Zohar Manna’s web page, zm/ ; look at the class web site for a link to the initial chapters of Volume III. 16-1 Volume III Progress Progress properties: Temporal logic plays a more prominent role and fairness becomes important. Property hierarchy: 16-2 Response under Justice (Chapter 1) Progress Properties We will consider deductive methods to prove response properties (which are also applicable to obligation and guarantee properties since these are subclasses) Response properties are those properties that can be expressed by a formula of the formula of the form 0 1 p for a past formula p . 16-3 Response formulas The verification rules presented assume that the response property is expressed by a response formula p 1 q for past formulas p and q . Note: Response formula expresses a response property because of the equivalence p 1 q 0 1 (( ¬ p ) B q ) Every response property can be expressed by a response formula due to the equivalence 0 1 q t 1 q 16-4

This preview has intentionally blurred sections. Sign up to view the full version.

Overview We consider the simple case where p , q are assertions. The proof of a response property p 1 q often relies on the identification of one or more so-called helpful transitions . We consider three cases: 1. Rule resp-j (single-step response under justice) A single helpful transition τ h suffices to establish the property p q τ h 16-5 Overview (Cont’d) 2. Rule chain-j (chain rule under justice) A fixed number of helpful transitions (independent of the value of variables) suffices to establish the property τ h n τ h n - 1 q τ h 1 p ϕ n - 1 ϕ 1 16-6 Overview (Cont’d) 3. Rule well-j (well-founded response under justice) The number of helpful transitions required to estab- lish the property is unbounded q p 16-7 Overview (Cont’d) In all cases we will be able to use verification diagrams to represent the proof. In practice, verification diagrams are often the preferred way to prove progress properties, because they represent the temporal structure of the program relative to the property. 16-8
Single-step rule (Motivation) p 1 q ϕ En ( τ h ) q τ h p Justice requirement: it is not the case that a just transi- tion is continuously enabled but never taken. 16-9 Single-step rule For assertions p , q , ϕ , and helpful transition τ h ∈ J , J1. p q ϕ J2. { ϕ } T { q ϕ } J3. { ϕ } τ h { q } J4. ϕ En ( τ h ) p 1 q Premise J2 requires all transitions to preserve ϕ (or es- tablish q , in which case we are done).

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• '
• NoProfessor
• Function composition, J2, helpful transition

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern