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Resource Bisimilarity in Petri Nets is Decidable

Lomazova Irina, Bashkin Vladimir, Jančar Petr

Fundamenta Informaticae

2022

Vol. 186, nr 1-4

175--194

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.

On-the-fly diagnosability analysis of bounded and unbounded labeled Petri nets using verifier nets

Li B., Khlif-Bouassida M., Toguéyni A.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 2

269--281

This paper considers the problem of diagnosability analysis of discrete event systems modeled by labeled Petri nets (LPNs). We assume that the LPN can be bounded or unbounded with no deadlock after firing any fault transition. Our approach is novel and presents the on-the-fly diagnosability analysis using verifier nets. For a given LPN model, the verifier net and its reachability graph (for a bounded LPN) or coverability graph (for an unbounded LPN) are built on-the-fly and in parallel for diagnosability analysis. As soon as a diagnosability decision is established, the construction is stopped. This approach achieves a compromise between computation limitations due to efficiency and combinatorial explosion and it is useful to implement an engineering approach to the diagnosability analysis of complex systems.