Some Congruence Properties for pi-calculus Bisimilarities
Résumé
Both for interleaving and for non-interleaving semantics, several variants of a $\pi$-calculus bisimilarity can be given which differ on the requirements imposed on name instantiations. Examples are the {\em late, early, open} and {\em ground} variants. The ground variant is the simplest because it places no requirements on name instantiations. With the exception of open bisimilarities, none of the bisimilarity considered in the literature is a congruence relation on the full $\pi$-calculus language. We show that in the case of (certain forms of) % the (non-interleaving) {\em causal bisimulation } the late, early, open and ground variants coincide and are congruence relations in the sublanguage of the $\pi$-calculus without matching. We also show that to obtain the same results in the case of the interleaving bisimilarity, in addition to forbidding matching it is necessary to constrain the output prefix.