Resource Bisimilarity in Petri Nets is Decidable

Issue title: Special Issue of Invited Papers in Honor of the Boris Trakhtenbrot Centenary

Guest editors: Arnon Avron, Nachum Dershowitz and Alexander Rabinovich

Article type: Research Article

Authors: Lomazova, Irina A.^{a; *} | Bashkin, Vladimir A.^b | Jančar, Petr^b

Affiliations: [a] ialomazova@gmail.com | [b] Dept. of Computer Science, Faculty of Science, Palacký University, Olomouc, Czechia. petr.jancar@upol.cz

Correspondence: [*] Address for correspondence: ialomazova@gmail.com

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.

Keywords: labeled Petri nets, bisimulation, congruence, decidability, resource bisimilarity

DOI: 10.3233/FI-222125

Journal: Fundamenta Informaticae, vol. 186, no. 1-4, pp. 175-194, 2022