Discrete Event Dynamic Systems

, Volume 17, Issue 2, pp 133–158 | Cite as

Reachability Problems and Abstract State Spaces for Time Petri Nets with Stopwatches

  • Bernard Berthomieu
  • Didier Lime
  • Olivier H. Roux
  • François Vernadat


Several extensions of Time Petri nets (TPNs) have been proposed for modeling suspension and resumption of actions in timed systems. We first introduce a simple class of TPNs extended with stopwatches (SwTPNs), and present a semi-algorithm for building exact representations of the behavior of SwTPNs, based on the known state class method for Time Petri nets. Then, we prove that state reachability in SwTPNs and all similar models is undecidable, even when bounded, which solves an open problem. Finally, we discuss overapproximation methods yielding finite abstractions of their behavior for a subclass of bounded SwTPNs, and propose a new one based on a quantization of the polyhedra representing temporal information. By adjusting a parameter, the exact behavior can be approximated as closely as desired. The methods have been implemented, experiments are reported.


Time Petri nets Stopwatches State classes Reachability Decidability Approximation Real-time systems modeling and verification 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alur R, Courcoubetis C, Halbwachs N, Henzinger T, Ho P-H, Nicollin X, Oliver A, Sifakis J, Yovine S (1995) The algorithmic analysis of hybrid systems. Theor Comp Sci 138:3–34zbMATHCrossRefGoogle Scholar
  2. Berthomieu B (2001) La méthode des classes d’états pour l’analyse des réseaux Temporels – Mise en œuvre, Extension à la multi-sensibilisation. Proc. Modélisation des Systèmes Réactifs, Toulouse, France, OctoberGoogle Scholar
  3. Berthomieu B, Diaz M (1991) Modeling and verification of time dependent systems using Time Petri Nets. IEEE Trans Softw Eng 17(3):259–273, MarchCrossRefMathSciNetGoogle Scholar
  4. Berthomieu B, Menasche M (1983) An enumerative approach for analyzing Time Petri Nets. IFIP Congr Ser 9:41–46Google Scholar
  5. Berthomieu B, Ribet P-O, Vernadat F (2004) The tool TINA – Construction of abstract state spaces for Petri Nets and Time Petri Nets. Int J Prod Res 42(14):2741–2756, 15 JulyzbMATHCrossRefGoogle Scholar
  6. Berthomieu B, Vernadat F (2003) State class constructions for branching analysis of Time Petri Nets. In: Proceedings tools and algorithms for the construction and analysis of systems, vol 2619. Springer LNCSGoogle Scholar
  7. Boucheneb H, Hadjidj R (2004) Towards optimal CTL * model checking of Time Petri nets. In: Proceedings of 7th workshop on discrete events systems, Reims, France, SeptemberGoogle Scholar
  8. Bucci G, Fedeli A, Sassoli L, Vicario E (2004) Time state space analysis of real-time preemptive systems. IEEE Trans Softw Eng 30(2):97–111, FebruaryCrossRefGoogle Scholar
  9. Cassez F, Larsen KG (2000) The impressive power of stopwatches. In: 11th international conference on concurrency theory, University Park, PA, USA, vol 1877. Springer LNCS, pp 138–152Google Scholar
  10. Čerāns K (1992) Algorithmic problems in analysis of real time system specifications, Thesis, University of LatviaGoogle Scholar
  11. Daws C, Tripakis S (1998) Model checking of real-time reachability properties using abstractions. In: Proceedings tools and algorithms for the construction and analysis of systems (TACAS’1998), vol 1384. Springer LNCSGoogle Scholar
  12. Gardey G, Lime D, Magnin M, Roux OH (2005) Roméo: a tool for analyzing time Petri nets. In: 17th international conference on computer aided verification, CAV’05, vol 3576. Springer LNCS, JulyGoogle Scholar
  13. Henzinger TA, Kopke PW, Puri A, Varaiya P (1995) What’s decidable about hybrid automata? In: Proceedings of the 27th annual symposium on theory of computing, ACM Press, pp 373–382Google Scholar
  14. Jeannet B (2002) The Polka Convex Polyhedra library, Edition 2.0.1,, IRISA, Rennes
  15. Jones ND, Landweber LH, Lien YE (1977) Complexity of some problems in Petri Nets. Theor Comp Sci 4:277–299zbMATHCrossRefMathSciNetGoogle Scholar
  16. Lime D, Roux OH (2003) Expressiveness and analysis of scheduling extended time Petri nets. In: 5th IFAC international conference on fieldbus systems and their applications (FET’03), Elsevier Science, JulyGoogle Scholar
  17. Merlin PM (1974) A study of the recoverability of computing systems. PhD Thesis, IrviveGoogle Scholar
  18. Minsky M (1961) Recursive unsolvability of post’s problem. Ann of Math 74:437–454CrossRefMathSciNetGoogle Scholar
  19. Roux OH, Déplanche A-M (2002) A t-time Petri net extension for real time task scheduling modeling. Eur Journal of Automation (JESA)Google Scholar
  20. Roux OH, Lime D (2004) Time Petri nets with inhibitor hyperarcs. Formal semantics and state space computation. In: Proceedings international conference on applications and theory of petri nets (ICATPN’04), Bologna, ItalyGoogle Scholar
  21. Schrijver A (1986) Theory of linear and integer programming. Wiley, New YorkzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Bernard Berthomieu
    • 1
  • Didier Lime
    • 2
  • Olivier H. Roux
    • 2
  • François Vernadat
    • 1
  1. 1.LAAS-CNRSToulouseFrance
  2. 2.IRCCyN1, rue de la NoëNantesFrance

Personalised recommendations