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Algebra of communicating processes with abstraction. (English) Zbl 0579.68016
This paper presents an equational axiom system $$ACP_{\tau}$$, for communicating processes with silent actions ($$\tau$$-steps). The system is an extension of ACP, Algebra of Communicating Processes [see the authors, Inf. Control 60, 109-137 (1984)] with Milner’s $$\tau$$-laws [see R. Milner, A calculus of communicating processes (Berlin 1980; Zbl 0452.68027)] and an explicit abstraction (’hiding’) operator. By means of a model of finite acyclic process graphs syntactic properties such as consistency and conservativity over ACP are proved. Also, the Expansion Theorem (which breaks down a parallel composition of n processes) is proved. By means of a term rewriting analysis using Dershowitz’s recursive path orderings, termination of rewriting terms according to the $$ACP_{\tau}$$ axioms is proved.

##### MSC:
 68N25 Theory of operating systems 68Q60 Specification and verification (program logics, model checking, etc.) 68Q45 Formal languages and automata 68Q65 Abstract data types; algebraic specification 68Q55 Semantics in the theory of computing
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