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Symbolic Unfolding of Parametric Stopwatch Petri Nets

  • Louis-Marie Traonouez
  • Bartosz Grabiec
  • Claude Jard
  • Didier Lime
  • Olivier H. Roux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6252)

Abstract

This paper proposes a new method to compute symbolic unfoldings for safe Stopwatch Petri Nets (SwPNs), extended with time parameters, that symbolically handle both the time and the parameters.

We propose a concurrent semantics for (parametric) SwPNs in terms of timed processes à la Aura and Lilius. We then show how to compute a symbolic unfolding for such nets, as well as, for the subclass of safe time Petri nets, how to compute a finite complete prefix of this unfolding.

Our contribution is threefold: unfolding in the presence of stopwatches or parameters has never been addressed before. Also in the case of time Petri nets, the proposed unfolding has no duplication of transitions and does not require read arcs and as such its computation is more local. Finally the unfolding method is implemented (for time Petri nets) in the tool Romeo.

Keywords

unfolding time Petri nets stopwatches parameters symbolic methods 

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References

  1. 1.
    Abdulla, P.A., Iyer, S.P., Nylen, A.: Unfoldings of unbounded Petri nets. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 495–507. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Aura, T., Lilius, J.: A causal semantics for time Petri nets. Theoretical Computer Science 243(2), 409–447 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Baldan, P., Busi, N., Corradini, A., Pinna, G.M.: Functorial concurrent semantics for Petri nets with read and inhibitor arcs. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 442–457. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Berthomieu, B., Diaz, M.: Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. on Soft. Eng. 17(3), 259–273 (1991)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Berthomieu, B., Lime, D., Roux, O.H., Vernadat, F.: Reachability problems and abstract state spaces for time Petri nets with stopwatches. Journal of Discrete Event Dynamic Systems - Theory and Applications (DEDS) 17(2), 133–158 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chatain, T., Jard, C.: Complete finite prefixes of symbolic unfoldings of safe time Petri nets. In: Donatelli, S., Thiagarajan, P.S. (eds.) ICATPN 2006. LNCS, vol. 4024, pp. 125–145. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Chatain, T., Jard, C.: Sémantique concurrente symbolique des réseaux de Petri saufs et dépliages finis des réseaux temporels. In: Proceedings of NOTERE, Tozeur, Tunisia. IEEE Computer Society Press, Los Alamitos (May-June 2010)Google Scholar
  8. 8.
    Esparza, J.: Model checking using net unfoldings. Science of Computer Programming 23, 151–195 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Esparza, J., Heljanko, K.: Unfoldings, A Partial-Order Approach to Model Checking. In: Monographs in Theoretical Computer Science. Springer, Heidelberg (2008)Google Scholar
  10. 10.
    Grabiec, B., Traonouez, L.-M., Jard, C., Lime, D., Roux, O.H.: Diagnosis using unfoldings of parametric time Petri nets. In: Proceedings of FORMATS, Vienna, Austria. LNCS. Springer, Heidelberg (to appear, September 2010)Google Scholar
  11. 11.
    Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? Journal of Computer and System Sciences 57, 94–124 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Khomenko, V., Koutny, M.: Branching processes of high-level Petri nets. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 458–472. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Lime, D., Roux, O.(H.): Formal verification of real-time systems with preemptive scheduling. Journal of Real-Time Systems 41(2), 118–151 (2009)CrossRefzbMATHGoogle Scholar
  14. 14.
    McMillan, K.L.: Using unfolding to avoid the state space explosion problem in the verification of asynchronous circuits. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 164–177. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  15. 15.
    Merlin, P.M.: A study of the recoverability of computing systems. PhD thesis, Dep. of Information and Computer Science, University of California, Irvine, CA (1974)Google Scholar
  16. 16.
    Traonouez, L.-M., Lime, D., Roux, O.H.: Parametric model-checking of stopwatch Petri nets. Journal of Universal Computer Science (J.UCS) 15(17), 3273–3304 (2009)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Louis-Marie Traonouez
    • 1
  • Bartosz Grabiec
    • 2
  • Claude Jard
    • 2
  • Didier Lime
    • 3
  • Olivier H. Roux
    • 3
  1. 1.Dipartimento di Sistemi e InformaticaUniversità di FirenzeItaly
  2. 2.ENS Cachan & INRIA, IRISAUniversité européenne de BretagneRennesFrance
  3. 3.École Centrale de Nantes & Université de Nantes, IRCCyNNantesFrance

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