The Complexity of Diagnosability and Opacity Verification for Petri Nets

  • Béatrice Bérard
  • Stefan Haar
  • Sylvain SchmitzEmail author
  • Stefan Schwoon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10258)


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 \(\mathsf {NL}\)-complete for finite state systems, \(\mathsf {PSPACE}\)-complete for safe Petri nets (even with fairness), and \(\mathsf {EXPSPACE}\)-complete for general Petri nets without fairness, while non diagnosability is inter-reducible with reachability when fault events are not weakly fair. Opacity is \(\mathsf {ESPACE}\)-complete for safe Petri nets (even with fairness) and undecidable for general Petri nets already without fairness.


Fault Transition Label Transition System Concurrent System Reachability Problem Weak Fairness 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Béatrice Bérard
    • 1
    • 2
  • Stefan Haar
    • 2
  • Sylvain Schmitz
    • 2
    Email author
  • Stefan Schwoon
    • 2
  1. 1.Sorbonne Universités, UPMC University Paris 06, LIP6ParisFrance
  2. 2.INRIA and LSV, CNRS and ENS CachanUniversité Paris-SaclayCachanFrance

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