# Pro Extensionist Library

By Clemens H. Cap

ISBN-10: 3322867633

ISBN-13: 9783322867636

ISBN-10: 332286765X

ISBN-13: 9783322867650

This ebook introduces a method calculus for parallel, disbursed and reactive platforms. It describes the conceptual foundations in addition to the mathematical idea in the back of a programming language, and a couple of software examples. the selected method offers a framework for knowing the semantics of parallel and allotted structures. additionally, it may be without delay utilized to sensible difficulties.

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Additional info for A Calculus of Distributed and Parallel Processes

Example text

Behaviours which are identical up to a renaming of states and transitions may thus be identified: 6For distributed transition systems, an initial behaviour will playa more important role. 46 Chapter 2. Transition Systems 27 Definition ISOMORPHISM OF BEHAVIOURS Let P = (8, T, -+) be a process. , J}) and (82 , T 2,-+2 ,n,jf) are called isomorphic, iff there exist bijections us: 8 1 -+ 8 2 and 'liT: Tl -+ T 2, such that t \IX, X' E 81, tET1: X-+ 1 X ' \IX E 8 1 : f~(us(X)) \It E T l : fj,(UT(t)) ¢:} UT(t) I us(X) -+2US(X) = fHX) = f}(t) ...

Sequential Composition 49 Now let B1 and B2 be two non-isomorphic maximal behaviours. Without loss of generality we may choose them in canonical form. Then, in the observing behaviours there exists a smallest natural number for which the observed states (and/or labels) differ. The state which is observed immediately before this state shows that the process must be non-deterministic . It may depend on the initial state whether non-determinism actually appears or not. 36 Definition OPERATIONAL SEMANTICS OF A PROCESS The operational semantics of a process P is given by its set of maximal behaviours.

8 b of states, i l < i2 < i3 < ... T(ti) is equal to t. A behaviour is called weakly (strongly) unfair, iff it is not weakly (strongly) fair. • Intuitively, behaviours are weakly fair, if it is not possible that a transition becomes enabled and stays enabled, but does not execute. 6. Fairness a transition is infinitely often enabled, but does not execute. For finite behaviours, fairness notions are meaningless. Strong fairness implies weak fairness. In the sense of this definition, the maximal behaviours from Examples 43 and 45 are strongly unfair, and in Example 44 we described a weakly unfair lIIaximal behaviour.