Correctness of concurrent processes

A new notion of correctness for concurrent processes is introduced and investigated. It is a relationship P sat S between process terms P built up from operators of CCS [Mi 80], CSP [Ho 85] and COSY [LTS 79] and logical formulas S specifying sets of finite communication sequences as in [Zw 89]. The definition of P sat S is based on a Petri net semantics for process terms [Ol 89]. The main point is that P sat S requires a simple liveness property of the net denoted by P. This implies that P is divergence free and externally deterministic. Process correctness P sat S determines a new semantic model for process terms and logical formulas. It is a modification ℜ* of the readiness semantics [OH 86] which is fully abstract with respect to the relation P sat S. The model ℜ* abstracts from the concurrent behaviour of process terms and certain aspects of their internal activity. In ℜ* process correctness P sat S boils down to semantic equality: ℜ*[P]=ℜ*[S]. The modified readiness equivalence is closely related to failure equivalence [BHR 84] and strong testing equivalence [DH 84].