Trace,failure and testing equivalences for communicating processes

A basic question in the theory of communicating processes is “When should two processes be considered equivalent?”. Attempts to answer this question have led to the concepts of observation equivalence, bisimulations, testing equivalence, failure equivalence, etc. The main point of this paper is to increase the understanding and motivation for two of these equivalences, namely failure and testing equivalences. The approach starts with the idea that the equivalence of processes should be reducible to the visible sequences of actions which a process performs in various contexts. This idea is implemented by a string-based semantic order for communicating processes where divergence is catastrophic. Under some assumptions about contexts, the resulting semantics is shown to be equivalent to theimproved failure semantics of Brookes and Roscoe⁽¹⁾ and also to themust testing-semantics of Hennessy and DeNicola.^(2–4) This characterization gives independent support for the appropriateness of failures and testing.