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The Congruences below Fair Testing with Initial Stability

When analysing behaviours of concurrent systems with process-algebraic methods, the notion of congruence plays a central role. It means an equivalence that remains valid if any subsystem is replaced by an equivalent one. It facilitates powerful compositional methods for the verification of systems. Unfortunately, so many congruences have been defined in the literature that it is difficult to know about them all. Furthermore, it may be that the best congruence for the task at hand is not yet known. The present study continues a line of research that tries to help the situation by choosing a region, listing all congruences in it, and proving that there are no others. The present study covers the congruences that are implied by fair testing equivalence with initial stability. The most important finding is that this region contains only few previously unknown congruences, and none of them seems interesting.