Flow Models of Distributed Computations: Three Equivalent Semantics for CCS

Abstract

We introduce three notions of computation for processes described as CCS (Calculus of Communicating Systems) terms. The first one uses an adaptation of the equivalence by permutations of Berry and Lèvy. In this setting, a computation is an equivalence class of sequences of transitions, up to the permutation of independent steps. The second notion of computation is given by means of an interpretation of CCS into a new class of event structures, the flow event structures. This can be seen as a reformulation of Winskel′s semantics for CCS by means of stable event structures. Here a computation is a configuration of an event structure. Finally, our third notion of computation is determined by an interpretation of CCS terms as Petri nets, and more precisely as flow nets. Here a computation is a set of events that are firable in sequence in the net. We then show that these three computation interpretations of CCS coincide, in the sense that for a given term, the three domains of computations are isomorphic. To this end we use an intermediary transition system for CCS, where the past is recorded; this appears to be a system of "trace computations," which provides another means of define the same abstract domain of computations.