Correctness of concurrent processes

Abstract

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 [24], CSP [18] and COSY [20] and logical formulas S specifying sets of finite communication sequences as in [38]. The definition of P sat S is based on a Petri net semantics for process terms [27]. 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 [28] 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 [7] and strong testing equivalence [9].