The Complexity of Diagnosability and Opacity Verification for Petri Nets

Béatrice Bérard 1, 2 Stefan Haar 3, 2 Sylvain Schmitz 2 Stefan Schwoon 3, 2
3 MEXICO - Modeling and Exploitation of Interaction and Concurrency
LSV - Laboratoire Spécification et Vérification [Cachan], ENS Cachan - École normale supérieure - Cachan, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8643
Abstract : Diagnosability and opacity are two well-studied problems in discrete-event systems. We revisit these two problems with respect to expressiveness and complexity issues. We first relate different notions of diagnosability and opacity. We consider in particular fairness issues and extend the definition of Germanos et al. [ACM TECS, 2015] of weakly fair diagnosability for safe Petri nets to general Petri nets and to opacity questions. Second, we provide a global picture of complexity results for the verification of diagnosability and opacity. We show that diagnosability is NL-complete for finite state systems, PSPACE-complete for safe Petri nets (even with fairness), and EXPSPACE-complete for general Petri nets without fairness, while non diagnosability is inter-reducible with reachability when fault events are not weakly fair. Opacity is ESPACE-complete for safe Petri nets (even with fairness) and undecidable for general Petri nets already without fairness.
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Béatrice Bérard, Stefan Haar, Sylvain Schmitz, Stefan Schwoon. The Complexity of Diagnosability and Opacity Verification for Petri Nets. Fundamenta Informaticae, Polskie Towarzystwo Matematyczne, 2018, 161 (4), pp.317--349. ⟨10.3233/FI-2018-1706⟩. ⟨hal-01852119⟩

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