On Asynchronous Communication Semantics

This paper presents some results concerning equational theories for an elementary calculus based on a fragment of Milner's-calculus. The system is interesting because it realises asynchronous message passing not by extending but reducing the original fragment, while preserving the computational power. The bisimulation based on a novel asynchronous transition system is introduced and studied. Presented results include congruence of the bisimilarity for the calculus, its relationship with two other asynchronous theories based on traces and failures, strict inclusion of its synchronous counterpart in the asynchronous theory, and the method called the I completion that transforms two asynchronously bisimilar terms into synchronously bisimilar ones.