Towards action-refinement in process algebras - Logic in Computer Science, 1989. LICS '89, Proceedings., Fourth Annual Symposium on

ory of concurrency; the symbol ; represents We present a simple process algebra which supports a form of refinement of an action by a process and address the question of an appropriate equivalence relation for it. The main result of the paper is that an adequate equivalence can be defined in a very intuitive manner and moreover can be axiomatized in much the same way as the standard behavioural equivalences. 1 Motivations sequential composition, + represents choice, 11 represents concurrency and * iteration. We wish to re-examine the formal semantic basis for this language. Specifically, we suggest a new semantic interpretation for the language, justify it from a behavioural point of view and show that it can be finitely axiomatized. For simplicity the Kleene closure operator * is omitted. However, part of our justification involves the introduction of a new operator. In formal language terms this operator stands for the homomorphic substitution of languages for variables, whereas from the perspective of process algebras it Regular expressions augmented by a shuffle operator, 11, have been used extensively in the represents the Of an action by a process. Indeed, much of the novelty of our theory of concurrency. This language of exapproach is in the formal treatment of this tended regular expressions consists of all the words which can be constructed from set operator and the investigation of the consequences of introducing it into the language. of generators using the symbols ;, +, 11 and *. Intuitively, the generators may be looked One simple semantic theory may be based upon as variables, as in formal language theon interpreting each expression as a language ory, or as uninterpreted actions, as in the theof strings over the generators in the same way 138 CH2753-2/89/0000/0138$01.00