Calculus of Communicating Systems

In automata theory, a process is modeled as an automaton. In Chaps. 6 and 7, we studied automata models for simple input/output systems with some extensions. In particular we discussed interaction of systems modeled by automata in Chap. 7. We modeled compositions of simple input/output systems as well as composition of reactive systems. In the latter instance, the composition is based on communication between automata, abstracted as “shared transitions”. The meaning of composed systems is understood from the behavior that can be observed. It is known to algebraists (Milner in A calculus for communicating systems, Lecture notes in computer science, vol 92. Springer, Berlin, 1980) that “the principle of compositionality of meaning requires an algebraic framework.” An algebra that allows equational reasoning about automata is the algebra of regular expressions. This is true for extended finite state machine models in which the semantics of concurrency includes all transitions, including synchronous communications whenever they occur.