Complexity of Checking Bisimilarity between Sequential and Parallel Processes
Decidability of bisimilarity for Process Algebra (PA) processes, arising by mixing sequential and parallel composition, is a long-standing open problem. The known results for subclasses contain the decidability of bisimilarity between basic sequential (i.e. BPA) processes and basic parallel processes (BPP). Here we revisit this subcase and derive an exponential-time upper bound. Moreover, we show that the problem if a given basic parallel process is inherently sequential, i.e. bisimilar with an unspecified BPA process, is PSPACE-complete. We also introduce a model of one-counter automata, with no zero tests but with counter resets, that capture the behaviour of processes in the intersection of BPA and BPP.
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