Resource Bisimilarity in Petri Nets is Decidable

TL;DR

This paper proves that resource bisimilarity in Petri nets, a relation indicating behavioral equivalence of resource components, is decidable, and provides an algorithm for checking this relation.

Contribution

It introduces an algorithm to decide resource bisimilarity in Petri nets, establishing its decidability, unlike resource similarity which was previously shown undecidable.

Findings

Resource bisimilarity is decidable in Petri nets.

An algorithm for checking resource bisimilarity is provided.

Example showing resource similarity does not imply bisimilarity.

Abstract

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