Synchronous Message Passing: On the Relation between Bisimulation and Refusal Equivalence

Abstract

To find congruence relations proved more difficult for synchronous message passing than for asynchronous message passing. As well-known, trace equivalence of state-machines, which represents to a congruence relation for asynchronous computations, is not a congruence relation for the classical operators of parallel composition as found in process algebras with synchronous message passing. In the literature we find two fundamentally different proposals to define congruence relations for synchronous message passing systems. One is using David Park’s bisimulation used by Robin Milner for his Calculus of Communicating Systems (CCS) which introduces a class of relations between systems with synchronous message passing, the other one is an equivalence relation, introduced by the denotational semantics, given by Tony Hoare for a process algebra like Communicating Sequential Processes (CSP), based on so-called readiness, refusal and failure concepts. In this little note we analyze the question whether the equivalence relation, introduced by denotational semantics is in fact a bisimulation.