A Complete Axiomatization for Branching Bisimulation Congruence of Finite-State Behaviours

This paper ooers a complete inference system for branching bisimulation congruence on a basic sublanguage of CCS for representing regular processes with silent moves. Moreover, complete axiomatizations are provided for the guarded expressions in this language, representing the divergence-free processes, and for the recursion-free expressions, representing the nite processes. Furthermore it is argued that in abstract interleaving semantics (at least for nite processes) branching bisimulation congruence is the nest reasonable congruence possible. The argument is that for closed recursion-free process expressions, in the presence of some standard process algebra operations like partially synchronous parallel composition and relabelling, branching bisimulation congruence is completely axiomatized by the usual axioms for strong congruence together with Milner's rst-law aa X = aX.