Branching Place Bisimilarity

05/07/2023

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by   Roberto Gorrieri, et al.

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Place bisimilarity is a behavioral equivalence for finite Petri nets, proposed in <cit.> and proved decidable in <cit.>. In this paper we propose an extension to finite Petri nets with silent moves of the place bisimulation idea, yielding branching place bisimilarity ≈_p, following the intuition of branching bisimilarity <cit.> on labeled transition systems. We also propose a slightly coarser variant, called branching d-place bisimilarity ≈_d, following the intuition of d-place bisimilarity in <cit.>. We prove that ≈_p and ≈_d are decidable equivalence relations. Moreover, we prove that ≈_d is strictly finer than branching fully-concurrent bisimilarity <cit.>, essentially because ≈_d does not consider as unobservable those τ-labeled net transitions with pre-set size larger than one, i.e., those resulting from (multi-party) interaction.