Process Algebra for Synchronous Communication

Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite system behind the communication algebra is shown to be confluent and terminating (modulo its permutative reductions). Further, some relationships are shown to hold between the four concepts of merging. Our aim is to contribute to the theory of concurrency, along the lines of an algebraic approach. The importance of a proper understanding of the basic issues concerning the behaviour of concurrent systems or processes, such as communication, is nowadays evident, and various formats have been proposed as a framework for concurrency. Without claiming historical precision, it seems safe to say that the proper development of an algebra of processes starts with the work of Milner (see his introductory work, (Milner, 1980)) in the form of his calculus of communicating systems (CCS). Milner states his aim in (Milner, 1983) in his own words: "In a definitive calculus there should be as few operators or combinators as possible, each of which embodies some distinct and intuitive idea, and which together give completely general expressive power." Milner (1983) proposes SCCS (synchronous CCS) based on four fundamental operators, and remarks: "These four operators obey (as we show) several algebraic identities. It is not too much to hope that a class of these identities may be isolated as axioms of an algebraic 'concurrency" theory, analogous (say) to rings or vector spaces." These two quotations denote precisely the general motivation underlying also the present paper. More specifically, in this paper we propose an algebra of processes based on elementary actions and on the operators + (alternative composition or 109 0019-9958/84 $3.00