Place Bisimilarity is Decidable, Indeed!

Place bisimilarity is a behavioral equivalence for finite Petri nets, proposed by Schnoebelen and co-workers in 1991. Differently from all the other behavioral relations proposed so far, a place bisimulation is not defined over the markings of a finite net, rather over its places, which are finitely many. However, place bisimilarity is not coinductive, as the union of place bisimulations may be not a place bisimulation. Place bisimilarity was claimed decidable in [1], even if the algorithm used to this aim [2] does not characterize this equivalence, rather the unique maximal place bisimulation which is also an equivalence relation; hence, its decidability was not proved. Here we show that it is possible to decide place bisimilarity with a simple, yet inefficient, algorithm, which essentially scans all the place relations (which are finitely many) to check whether they are place bisimulations. Moreover, we propose a slightly coarser variant, we call d-place bisimilarity, that we conjecture to be the coarsest equivalence, fully respecting causality and branching time, to be decidable on finite Petri nets.