Advertisement

Solving the Petri Nets Reachability Problem Using the Logical Abstraction Technique and Mathematical Programming

  • Thomas Bourdeaud’huy
  • Said Hanafi
  • Pascal Yim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3011)

Abstract

This paper focuses on the resolution of the reachability problem in Petri nets, using the logical abstraction technique and the mathematical programming paradigm. The proposed approach is based on an implicit exploration of the Petri net reachability graph. This is done by constructing a unique sequence of partial steps. This sequence represents exactly the total behavior of the net. The logical abstraction technique leads us to solve a constraint satisfaction problem. We also propose different new formulations based on integer and/or binary linear programming. Our models are validated and compared on large data sets, using Prolog IV and Cplex solvers.

Keywords

Integer Linear Program Constraint Satisfaction Problem Integer Linear Program Model Reachability Graph Reachability Problem 
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.
    Benasser, A.: L’accessibilité dans les réseaux de Petri: une approche basée sur la programmation par contraintes. PhD thesis, Université des sciences et technologies de Lille (2000)Google Scholar
  2. 2.
    Benasser, A., Yim, P.: Railway traffic planning with petri nets and constraint programming. JESA 33(8-9), 959–975 (1999)Google Scholar
  3. 3.
    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 (1986)Google Scholar
  4. 4.
    Bourdeaud’huy, T., Hanafi, S., Yim, P.: Résolution du problème d’accessibilité dans les réseaux de Petri par l’abstraction logique et la programmation mathématique. Technical report, L.A. G. I. S., Ecole Centrale de Lille (2004)Google Scholar
  5. 5.
    Briand, C.: Solving the car-sequencing problem using petri nets. In: International Conference on Industrial Engineering and Production Management, vol. 1, pp. 543–551 (1999)Google Scholar
  6. 6.
    Fernandez, J.-C., Jard, C., Jéron, T., Mounier, L.: “on the fly” verification of finite transition systems. Formal Methods in System Design (1992)Google Scholar
  7. 7.
    Gunnarsson, J.: Symbolic tools for verification of large scale DEDS. In: Proc. IEEE Int. Conf. on Systems, Man, and Cybernetics (SMC 1998), San Diego, CA, October 11-14, pp. 722–727 (1998)Google Scholar
  8. 8.
    Huber, P., Jensen, A.M., Jepsen, L.O., Jensen, K.: Towards reachability trees for high-level petri nets. In: Rozenberg, G. (ed.) APN 1984. LNCS, vol. 188, pp. 215–233. Springer, Heidelberg (1985)Google Scholar
  9. 9.
    Jaffar, J., Michaylov, Stuckey, P., Yap, R.: The clp(r) language and system. ACM Transactions on Programming Languages and Systems 14(3), 339–395 (1992)CrossRefGoogle Scholar
  10. 10.
    Keller, R.M.: Formal verification of parallel programs. Comm. of the ACM 19(7), 371–384 (1976)CrossRefzbMATHGoogle Scholar
  11. 11.
    Kosaraju, S.R.: Decidability and reachability in vector addition systems. In: Proc. of the 14th Annual ACM Symp. on Theory of Computing, pp. 267–281 (1982)Google Scholar
  12. 12.
    Lautenbach, K.: Linear algebraic techniques for place/transition nets. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 254, pp. 142–167. Springer, Heidelberg (1987)Google Scholar
  13. 13.
    Lee, D.Y., DiCesare, F.: Scheduling flexible manufacturing systems using petri nets and heuristic search. IEEE Transactions on Robotics and Automation 10(2), 123–132 (1994)CrossRefGoogle Scholar
  14. 14.
    Lindqvist, M.: Parameterized reachability trees for predicate/transition nets. In: Rozenberg, G. (ed.) APN 1993. LNCS, vol. 674, pp. 301–324. Springer, Heidelberg (1993)Google Scholar
  15. 15.
    Lipton, R.: The reachability problem requires exponential space. Technical report, Computer Science Dept., Yale University (1976)Google Scholar
  16. 16.
    Murata, T.: Petri nets: properties, analysis ans applications. In: Proceedings of the IEEE, vol. 77, pp. 541–580 (1989)Google Scholar
  17. 17.
    Parker, R.G., Rardin, R.L.: Discrete Optimization. Academic Press, London (1988)zbMATHGoogle Scholar
  18. 18.
    Valmari, A.: Stubborn sets for reduced state space generation. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 491–515. Springer, Heidelberg (1991)Google Scholar
  19. 19.
    Vernadat, F., Azéma, P., Michel, P.: Covering steps graphs. In: 17 th Int. Conf on Application and Theory of Petri Nets 1996 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thomas Bourdeaud’huy
    • 1
  • Said Hanafi
    • 2
  • Pascal Yim
    • 1
  1. 1.L.A.G.I.S., Ecole Centrale de Lille Cité ScientiqueVilleneuve d’Ascq CedexFrance
  2. 2.L.A.M.I.H., Université de ValenciennesValenciennes Cedex 9France

Personalised recommendations