Advertisement

Complete Finite Prefixes of Symbolic Unfoldings of Safe Time Petri Nets

  • Thomas Chatain
  • Claude Jard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4024)

Abstract

Time Petri nets have proved their interest in modeling real-time concurrent systems. Their usual semantics is defined in term of firing sequences, which can be coded in a (symbolic and global) state graph, computable from a bounded net. An alternative is to consider a “partial order” semantics given in term of processes, which keep explicit the notions of causality and concurrency without computing arbitrary interleavings. In ordinary place/transition bounded nets, it has been shown for many years that the whole set of processes can be finitely represented by a prefix of what is called the “unfolding”. This paper defines such a prefix for safe time Petri nets. It is based on a symbolic unfolding of the net, using a notion of “partial state”.

Keywords

Partial State Maximal State Extended Process Normal Disjunctive Form Extended Event 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kitai, T., Oguro, Y., Yoneda, T., Mercer, E., Myers, C.: Partial order reduction for timed circuit verification based on a level oriented model. IEICE Trans. E86-D(12), 2601–2611 (2001)Google Scholar
  2. 2.
    Penczek, W., Pólrola, A.: Abstractions and partial order reductions for checking branching properties of time Petri nets. In: Colom, J.-M., Koutny, M. (eds.) ICATPN 2001. LNCS, vol. 2075, pp. 323–342. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Chatain, T., Jard, C.: Time Supervision of Concurrent Systems Using Symbolic Unfoldings of Time Petri Nets. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 196–210. Springer, Heidelberg (2005); Extended version available in INRIA Research Report RR-5706Google Scholar
  4. 4.
    Aura, T., Lilius, J.: Time processes for time Petri nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 136–155. Springer, Heidelberg (1997)Google Scholar
  5. 5.
    Lilius, J.: Efficient state space search for time Petri nets. In: MFCS Workshop on Concurrency 1998. ENTCS, vol. 18. Elsevier, Amsterdam (1999)Google Scholar
  6. 6.
    McMillan, K.L.: A technique of state space search based on unfolding. Formal Methods in System Design 6(1), 45–65 (1995)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Esparza, J., Römer, S., Vogler, W.: An improvement of McMillan’s unfolding algorithm. Formal Methods in System Design 20(3), 285–310 (2002)MATHCrossRefGoogle Scholar
  8. 8.
    Bieber, B., Fleischhack, H.: Model checking of time Petri nets based on partial order semantics. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 210–225. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Fleischhack, H., Stehno, C.: Computing a finite prefix of a time Petri net. In: Esparza, J., Lakos, C.A. (eds.) ICATPN 2002. LNCS, vol. 2360, pp. 163–181. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Berthomieu, B., Diaz, M.: Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. Software Eng. 17(3), 259–273 (1991)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Semenov, A.L., Yakovlev, A.: Verification of asynchronous circuits using time Petri net unfolding. In: DAC, pp. 59–62. ACM Press, New York (1996)Google Scholar
  12. 12.
    Merlin, P., Farber, D.: Recoverability of communication protocols – implications of a theorical study. IEEE Transactions on Communications 24 (1976)Google Scholar
  13. 13.
    Engelfriet, J.: Branching processes of Petri nets. Acta Inf. 28(6), 575–591 (1991)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Chatain, T., Jard, C.: Symbolic diagnosis of partially observable concurrent systems. In: de Frutos-Escrig, D., Núñez, M. (eds.) FORTE 2004. LNCS, vol. 3235, pp. 326–342. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Best, E.: Structure theory of Petri nets: the free choice hiatus. In: Proceedings of an Advanced Course on Petri Nets: Central Models and Their Properties, Advances in Petri Nets 1986-Part I, London, UK, pp. 168–205. Springer, Heidelberg (1987)CrossRefGoogle Scholar
  16. 16.
    Baldan, P., Corradini, A., Montanari, U.: Contextual Petri nets, asymmetric event structures, and processes. Inf. Comput. 171(1), 1–49 (2001)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Vogler, W., Semenov, A.L., Yakovlev, A.: Unfolding and finite prefix for nets with read arcs. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 501–516. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Thomas Chatain
    • 1
  • Claude Jard
    • 2
  1. 1.IRISA/INRIARennesFrance
  2. 2.IRISA/ENS Cachan-BretagneBruzFrance

Personalised recommendations