Resource Bisimilarity in Petri Nets is Decidable

Petri nets are a popular formalism for modeling and analyzing distributed systems. Tokens in net models can represent the control flow state or resources produced/consumed by transition firings. We define resource as part (a submultiset) of markings call two equivalent when replacing one them with another any marking does not change observable behavior. consider similarity bisimilarity, congruent restrictions bisimulation equivalence on markings. Previously it was proved that (the largest congruence included equivalence) is undecidable. Here we present an algorithm checking thereby proving this relation bisimulation) decidable. also give example similar but bisimilar.