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Deciding bisimulation-like equivalences with finite-state processes. (English) Zbl 0974.68131
Summary: We show that characteristic formulae for finite-state systems up to bisimulation-like equivalences (e.g., strong and weak bisimilarity) can be given in the simple branching-time temporal logic $$EF.$$ Since $$EF$$ is a very weak fragment of the modal $$\mu$$-calculus, model checking with $$EF$$ is decidable for many more classes of infinite state systems. This yields 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 pushdown (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’).

##### MSC:
 68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
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##### References:
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