On the Reversibility of Well-Behaved Weighted Choice-Free Systems

  • Thomas Hujsa
  • Jean-Marc Delosme
  • Alix Munier-Kordon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8489)


A Petri net is reversible if its initial marking is a home marking, a marking reachable from any reachable marking. Under the assumption of well-behavedness we investigate the property of reversibility for strongly connected weighted Choice-Free Petri nets, nets which structurally avoid conflicts. Several characterizations of liveness and reversibility as well as exponential methods for building live and home markings are available for these nets. We provide a new characterization of reversibility leading to the construction in polynomial time of an initial marking with a polynomial number of tokens that is live and reversible. We also introduce a polynomial time transformation of well-formed Choice-Free systems into well-formed T-systems and we deduce from it a polynomial time sufficient condition of liveness and reversibility for well-formed Choice-Free systems. We show that neither one of these two approaches subsumes the other.


Reversibility well-behavedness polynomial conditions decomposition place-splitting transformation weighted Petri nets Choice-Free Fork-Attribution T-system 


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  1. 1.
    Lee, E.A., Messerschmitt, D.G.: Synchronous Data Flow. Proceedings of the IEEE 75(9), 1235–1245 (1987)CrossRefGoogle Scholar
  2. 2.
    Best, E., Darondeau, P.: Petri Net Distributability. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds.) PSI 2011. LNCS, vol. 7162, pp. 1–18. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Murata, T.: Petri Nets: Properties, Analysis and Applications. Proceedings of the IEEE 77(4), 541–580 (1989)CrossRefGoogle Scholar
  4. 4.
    Teruel, E., Colom, J.M., Silva, M.: Choice-Free Petri Nets: A Model for Deterministic Concurrent Systems with Bulk Services and Arrivals. IEEE Transactions on Systems, Man and Cybernetics, Part A 27(1), 73–83 (1997)CrossRefGoogle Scholar
  5. 5.
    Teruel, E., Chrzastowski-Wachtel, P., Colom, J.M., Silva, M.: On Weighted T-systems. In: Jensen, K. (ed.) ICATPN 1992. LNCS, vol. 616, pp. 348–367. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  6. 6.
    Barkaoui, K., Petrucci, L.: Structural Analysis of Workflow Nets with Shared Resources. In: van der Aalst, W.M.P., De Michelis, G., Ellis, C.A. (eds.) Proceedings of Workflow Management: Net-Based Concepts, Models, Techniques and Tools (WFM 1998). Computing Science Report, vol. 98/7, pp. 82–95 (1998)Google Scholar
  7. 7.
    Teruel, E., Silva, M.: Liveness and Home States in Equal Conflict Systems. In: Marsan, M.A. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 415–432. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  8. 8.
    Recalde, L., Teruel, E., Silva, M.: Modeling and Analysis of Sequential Processes that Cooperate through Buffers. IEEE Transactions on Robotics and Automation 14(2), 267–277 (1998)CrossRefGoogle Scholar
  9. 9.
    Berthelot, G., Lri-Iie: Checking Properties of Nets Using Transformations. In: Rozenberg, G. (ed.) APN 1985. LNCS, vol. 222, pp. 19–40. Springer, Heidelberg (1986)CrossRefGoogle Scholar
  10. 10.
    Berthelot, G.: Transformations and Decompositions of Nets. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 254, pp. 359–376. Springer, Heidelberg (1987)Google Scholar
  11. 11.
    Colom, J., Teruel, E., Silva, M., Haddad, S.: Structural Methods. In: Petri Nets for Systems Engineering, pp. 277–316. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Memmi, G., Roucairol, G.: Linear Algebra in Net Theory. In: Brauer, W. (ed.) Net Theory and Applications. LNCS, vol. 84, pp. 213–223. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  13. 13.
    Sifakis, J.: Structural Properties of Petri Nets. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 474–483. Springer, Heidelberg (1978)CrossRefGoogle Scholar
  14. 14.
    Teruel, E., Silva, M.: Structure theory of Equal Conflict systems. Theoretical Computer Science 153(1&2), 271–300 (1996)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Keller, R.M.: A Fundamental Theorem of Asynchronous Parallel Computation. In: Feng, T.-Y. (ed.) Parallel Processing. LNCS, vol. 24, pp. 102–112. Springer, Heidelberg (1975)CrossRefGoogle Scholar
  16. 16.
    Best, E., Darondeau, P.: Decomposition Theorems for Bounded Persistent Petri Nets. In: van Hee, K.M., Valk, R. (eds.) PETRI NETS 2008. LNCS, vol. 5062, pp. 33–51. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Lien, Y.E.: Termination Properties of Generalized Petri Nets. SIAM Journal on Computing 5(2), 251–265 (1976)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Delosme, J.M., Hujsa, T., Munier-Kordon, A.: Polynomial Sufficient Conditions of Well-behavedness for Weighted Join-Free and Choice-Free Systems. In: Proceedings of the 13th International Conference on Application of Concurrency to System Design (ACSD 2013), pp. 90–99 (2013)Google Scholar
  19. 19.
    Hujsa, T., Delosme, J.M., Munier-Kordon, A.: Polynomial Sufficient Conditions of Well-behavedness and Home Markings in Subclasses of Weighted Petri Nets. Transactions on Embedded Computing Systems (to appear, 2014)Google Scholar
  20. 20.
    Marchetti, O., Munier-Kordon, A.: A Sufficient Condition for the Liveness of Weighted Event Graphs. European Journal of Operational Research 197(2), 532–540 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Thomas Hujsa
    • 1
  • Jean-Marc Delosme
    • 2
  • Alix Munier-Kordon
    • 1
  1. 1.Sorbonne Universités, UPMC Paris 06, UMR 7606, LIP6ParisFrance
  2. 2.Université d’Evry-Val-D’Essonne, IBISCEvryFrance

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