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On liveness and controlled siphons in Petri nets

  • Kamel Barkaoui
  • Jean-François Pradat-Peyre
Full Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1091)

Abstract

Structure theory of Petri nets investigates the relationship between the behavior and the structure of the net. Contrary to linear algebraic techniques, graph based techniques fully exploit the properties of the flow relation of the net (pre and post sets). Liveness of a Petri net is closely related to the validation of certain predicates on siphons. In this paper, we study thoroughly the connections between siphons structures and liveness. We define the controlled-siphon property that generalizes the well-known Commoner's property, since it involves both traps and invariants notions. We precise some structural conditions under which siphons cannot be controlled implying the structural non-liveness. These conditions based on local synchronization patterns cannot be captured by linear algebraic techniques. We establish a graph-theoretical characterization of the non-liveness under the controlled-siphon property. Finally, we prove that the controlled-siphon property is a necessary and sufficient liveness condition for simple nets and asymmetric choice nets. All these results are illustrated by significant examples taken from literature.

Keywords

Input Place Valuation Versus Minimal Siphon Initial Marking Rank Theorem 
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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References

  1. 1.
    K. Barkaoui, J.M Couvreur, and C. Duteilhet. On liveness in extended non self-controlling nets in application and theory of Petri nets. LNCS, 935, 1995.Google Scholar
  2. 2.
    K. Barkaoui and B. Lemaire. An effective characterization of minimal deadlocks and traps based on graph theory. 10th ICATPN, 1989.Google Scholar
  3. 3.
    K. Barkaoui and M. Minoux. A polynomial time graph algorithm to decide liveness of some basic classes of bounded Petri nets. LNCS, No. 616:62–75, 1992.Google Scholar
  4. 4.
    E. Best. Structure theory of Petri nets: The free choice hiatus. In G. Rozenberg W. Brauer, W. Resig, editor, LNCS, volume No. 255. Springer-Verlag, 1986.Google Scholar
  5. 5.
    G.W. BRAMS. Réseaux de Petri: Theorie et pratique. Masson, 1983.Google Scholar
  6. 6.
    J. Desel. A proof of the rank theorem for extended free choice nets. LNCS, No. 616:134–153, 1992.Google Scholar
  7. 7.
    F. Dicesare, G. Harhalakis, J.M. Proth, M. Silva, and F.B. Vernadat. Practice of Petri Nets in Manufacturing. Chapman-Hall, 1995.Google Scholar
  8. 8.
    J. Esparza and M. Silva. A polynomial-time algorithm to decide liveness of bounded free-choice nets. T.C.S, N 102:185–205, 1992.Google Scholar
  9. 9.
    M.H.T. Hack. Analysis of production schemata by Petri nets. In Cambridge, Mass.: MIT, MS Thesis, 1974.Google Scholar
  10. 10.
    M. Jantzen and R. Valk. Formal properties of P/T nets. LNCS, No. 84, 1981.Google Scholar
  11. 11.
    P. Kemper and F. Bause. An efficient polynomial-time algorithm to decide liveness and boundedness of free-choice nets. LNCS, No. 616:263–278, 1992.Google Scholar
  12. 12.
    W. Reisig. EATCS-An Introduction to Petri Nets. Springer-Verlag, 1983.Google Scholar
  13. 13.
    H. Ridder and K. Lautenbach. Liveness in bounded Petri nets which are covered by t-invariants. LNCS, No. 815:358–375, 1994.Google Scholar
  14. 14.
    M. Zhou and F. DiCesare. Petri nets Synthesis for Discrete Event Control of Manufacturing Systems. Kluwer Academic, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Kamel Barkaoui
    • 1
  • Jean-François Pradat-Peyre
    • 1
  1. 1.Laboratoire CEDRICConservatoire National des Arts et MétiersParis 75141 Cedex 03France

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