Affiliations: [a] Sorbonne Universités, UPMC Univ. Paris 06, LIP6, CNRS, Paris, France. beatrice.berard@lip6.fr | [b] INRIA and LSV, ENS Paris-Saclay and CNRS, Université Paris-Saclay, France. stefan.haar@inria.fr | [c] LSV, ENS Paris-Saclay and CNRS, Université Paris-Saclay, France. schmitz@lsv.fr | [d] LSV, ENS Paris-Saclay and CNRS, Université Paris-Saclay, and INRIA, France. schwoon@lsv.fr
Correspondence:
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Address for correspondence: LSV, ENS Paris-Saclay, 61 avenue du Président Wilson, 94230 Cachan, France
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 convergent 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.
Keywords: Diagnosability, Opacity, Verification, Complexity, Petri nets
