Delay-Dependent Partial Order Reduction Technique for Time Petri Nets

  • Hanifa Boucheneb
  • Kamel Barkaoui
  • Karim Weslati
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8711)


Partial order reduction techniques aim at coping with the state explosion problem by reducing, while preserving the properties of interest, the number of transitions to be fired from each state of the model. For (time) Petri nets, the selection of these transitions is, generally, based on the structure of the (underlying) Petri net and its current marking. This paper proposes a partial order reduction technique for time Petri nets (TPN in short), where the selection procedure takes into account the structure, including the firing intervals, and the current state (i.e., the current marking and the firing delays of the enabled transitions). We show that our technique preserves non-equivalent firing sequences of the TPN. Therefore, its extension to deal with LTL − X properties is straightforward, using the well established methods based on the stuttering equivalent sequences.


Partial Order Model Check Canonical Form State Class Partial Order Reduction 
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.


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  1. 1.
    Belluomini, W., Myers, C.J.: Timed state space exploration using POSETs. IEEE Transactions on Computer-Aided Design of Integrated Circuits 19(5), 501–520 (2000)Google Scholar
  2. 2.
    Bengtsson, J.: Clocks, DBMs and States in Timed Systems. PhD thesis, Dept. of Information Technology, Uppsala University (2002)Google Scholar
  3. 3.
    Bengtsson, J.E., Jonsson, B., Lilius, J., Yi, W.: Partial order reductions for timed systems. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 485–500. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: The expressive power of time Petri nets. Theoretical Computer Science 474, 1–20 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Berthomieu, B., Vernadat, F.: State class constructions for branching analysis of time Petri nets. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 442–457. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Boucheneb, H., Barkaoui, K.: Reducing interleaving semantics redundancy in reachability analysis of time Petri nets. ACM Transactions on Embedded Computing Systems (TECS) 12(1), 259–273 (2013)CrossRefGoogle Scholar
  7. 7.
    Boucheneb, H., Gardey, G., Roux, O.H.: TCTL model checking of time Petri nets. Logic and Computation 19(6), 1509–1540 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Boucheneb, H., Hadjidj, R.: CTL* model checking for time Petri nets. Theoretical Computer Science TCS 353(1-3), 208–227 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Boucheneb, H., Lime, D., Roux, O.H.: On multi-enabledness in time Petri nets. In: Colom, J.-M., Desel, J. (eds.) PETRI NETS 2013. LNCS, vol. 7927, pp. 130–149. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Boucheneb, H., Rakkay, H.: A more efficient time Petri net state space abstraction useful to model checking timed linear properties. Fundamenta Informaticae 88(4), 469–495 (2008)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Boyer, M., Diaz, M.: Multiple-enabledness of transitions in time Petri nets. In: 9th IEEE International Workshop on Petri Nets and Performance Models, pp. 219–228 (2001)Google Scholar
  12. 12.
    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
  13. 13.
    Delfieu, D., Sogbohossou, M., Traonouez, L.M., Revol, S.: Parameterized study of a time Petri net. In: Cybernetics and Information Technologies, Systems and Applications: CITSA, pp. 89–90 (2007)Google Scholar
  14. 14.
    Godefroid, P.: Partial-Order Methods for the Verification of Concurrent Systems. LNCS, vol. 1032, pp. 1–142. Springer, Heidelberg (1996)Google Scholar
  15. 15.
    Håkansson, J., Pettersson, P.: Partial order reduction for verification of real-time components. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 211–226. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Lilius, J.: Efficient state space search for time Petri nets. In: MFCS Workshop on Concurrency Algorithms and Tools. ENTCS, vol. 8, pp. 113–133 (1998)Google Scholar
  17. 17.
    Lugiez, D., Niebert, P., Zennou, S.: A partial order semantics approach to the clock explosion problem of timed automata. Theoretical Computer Science TCS 345(1), 27–59 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Minea, M.: Partial order reduction for model checking of timed automata. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 431–446. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  19. 19.
    Peled, D.: All from one, one for all: on model checking using representatives. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 409–423. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  20. 20.
    Peled, D., Wilke, T.: Stutter invariant temporal properties are expressible without the next-time operator. Information Processing Letters 63(5), 243–246 (1997)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Romulo, F., Raimundo, B., Paulo, M.: Analysis of real-time scheduling problems by single step and maximal step semantics for time petri net models. In: 3rd Brazilian Symposium on Computing Systems Engineering (SBESC), pp. 107–112 (2013)Google Scholar
  22. 22.
    Salah, R.B., Bozga, M., Maler, O.: On interleaving in timed automata. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 465–476. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  23. 23.
    Semenov, A., Yakovlev, A.: Verification of asynchronous circuits using time Petri net unfolding. In: 33rd Annual Conference on Design Automation (DAC), pp. 59–62 (1996)Google Scholar
  24. 24.
    Valmari, A., Hansen, H.: Can stubborn sets be optimal? In: Lilius, J., Penczek, W. (eds.) PETRI NETS 2010. LNCS, vol. 6128, pp. 43–62. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  25. 25.
    Yoneda, T., Ryuba, H.: CTL model checking of time Petri nets using geometric regions. EICE Trans. Inf. & Syst. E-99D(3), 297–306 (1998)Google Scholar
  26. 26.
    Yoneda, T., Schlingloff, B.H.: Efficient verification of parallel real-time systems. Formal Methods in System Design 11(2), 187–215 (1997)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hanifa Boucheneb
    • 1
    • 2
  • Kamel Barkaoui
    • 2
  • Karim Weslati
    • 1
  1. 1.Laboratoire VeriForm, Department of Computer Engineering and Software EngineeringÉcole Polytechnique de MontréalMontréalCanada
  2. 2.Laboratoire CEDRICConservatoire National des Arts et MétiersParis Cedex 03France

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