By Colin Stirling

ISBN-10: 1441931538

ISBN-13: 9781441931535

ISBN-10: 1475735502

ISBN-13: 9781475735505

This is often an introductory publication at the modal and temporal houses of strategies. In a transparent and well-organized remedy the ebook presents an creation to: -process calculi for modeling concurrent platforms -modal homes of platforms and bisimulation equivalence offered when it comes to video games -temporal homes of structures -modal mu-calculus as a basic objective temporal good judgment -verification concepts for displaying temporal homes of structures, together with verification as a online game; version checking by way of game-theoretic algorithms; tablaux as unwindings of winning ideas; compositional verification, in particular in relation to countless structures. using video games for either equivalence and version checking is conceptually clearer than different techniques and the book's well-thought-out constitution and illuminating examples make this e-book well-suited for and complicated undergraduate or graduate point direction in version checking or formal tools of verification.

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**Extra info for Modal and Temporal Properties of Processes**

**Sample text**

2. Show that Cop realises the property [in(m)] ([i] {(-))tt /\ [-out(m)] ff) and Protocol fails to have this property. 3. - is closed under complement. F= * iff Div F= <1>. Prove that for all in MO,!. , Cto F= iff Count F= <1> . 4. Prove that, for all in MO, 0 5. 6. Which of the following MO,!. formulas are realisable? a. ] «tick))tt /\ {( t)) {(tick))tt) b. [K i] {(tl) [tick] ff c. [K] ({(t)) {(tick))tt /\ [] [tick] ff) d. 2 Interactive games . 6 Equivalence checking 77 Example processes were defined in Chapter 1, and in Chapter 2 modallogics were introduced for expressing their capabilities. *

This remains true for the following restricted process language, where P ranges over process names, a over actions, and lover finite sets of indices . Ei : i E I} I EI I E2 I E\{a} A process expression is either a name, a finite sum ofprocess expressions, a parallel composition of process express ions, or a restricted process expression. A (closed) process is given as a finite family {Pi ~ Ei : I ::: i ::: n} of definitions, where all the process names in each Ei belong to the set {PI , . . , Pn }.

We assume the following abbreviations. [-K] <1> ((-K}) <1> def = [0- K] def ((0 - K)} = Therefore, [-] and (( -)} are abbreviations of [0] and ((O}). D~' v re al'ises it, process D~' v def Modal formulas can be used to express notions that are basic to the theory of CSP [31]. a; provided it has the property ((al}) , , . ((an}}tt . ]ff). The formula [K] ff expresses that the observable set of actions K is a "refusal," since a realizing process is unable to perform observable actions belonging to K.

### Modal and Temporal Properties of Processes by Colin Stirling

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