Deciding and axiomatizing weak ST bisimulation for a process algebra with recursion and action refinement

Abstract

Due to the complex nature of bisimulation equivalences that express some form of history dependence, it turned out to be problematic to decide them over nontrivial classes of recursive systems. Moreover, to the best of our knowledge, the problem of axiomatizing them over such classes of systems has never been solved. In this article, we face this problem in the case of weak ST bisimulation, an equivalence that expresses the execution of an action as the combination of the two interdependent events of action start and action termination and that supports the operation of action refinement. We first consider a basic process algebra with CSP multiway synchronization and recursion and we show that a simple technique based on static names is sufficient to decide weak ST bisimulation over processes that are finite state according to the standard interleaving semantics. Then we introduce a different technique based on dynamic names and on the new idea of compositional level-wise renaming of actions (which produces semantic models via SOS such that weak ST bisimulation can be established through standard weak bisimulation) and we show that it can be applied to decide and axiomatize weak ST bisimulation over the same class of processes. Finally, we introduce a third technique based on pointers, updated according to a pseudo-stack discipline, which preserves the possibility of deciding and axiomatizing weak ST bisimulation also when an action refinement operator is considered.