Deciding bisimulation-like equivalences with finite-state processes

Abstract

We design a general method for proving decidability of bisimulation-like equivalences between infinite-state processes and finite-state ones. We apply this method to the class of PAD processes, which strictly subsumes PA and push-down (PDA) processes, showing that a large class of bisimulation-like equivalences (including e.g. strong and weak bisimilarity) is decidable between PAD and finite-state processes. On the other hand, we also demonstrate that no ‘reasonable’ bisimulation-like equivalence is decidable between state-extended PA processes and finite-state ones. Furthermore, weak bisimilarity with finite-state processes is shown to be undecidable even for state-extended BPP (which are also known as ‘parallel pushdown processes’).KeywordsModel CheckTransition SystemReach ProblemModel Check ProblemCounter MachineThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.