A new technique for finding a generating family of siphons, traps and st-components. Application to colored Petri nets

  • J. Ezpeleta
  • J. M. Couvreur
  • M. Silva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 674)


In this paper we propose a new solution to the problem of finding generating families of siphons (structural dead-locks in classical terminology), traps and st-components in Petri Nets. These families are obtained as solutions of some systems of linear inequalities. Their transformation into a system of linear equations allows to interpret the technique as follows: traps (siphons, st-components) of a net N are deduced from the support of psemiflows of a transformed net NΘ(NΣ,NΣΘ).

One of the basic advantages of the proposed technique is its direct applicability to colored nets, allowing the symbolic computation of traps (siphons, st-components), whose definitions are introduced in this work.


Petri net colored Petri net siphon trap st-component p-semiflow 


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  1. [AlTo 85]
    ALAIWAN H., TOUDIC J.F., Recherche des semi-flots, des verrous et des trappes dans les réseaux de Petri, TSI.vol. 4,n.1, 1985, p. 103–112.Google Scholar
  2. [BaLe 89]
    BARKAOUI K., LEMAIRE B., An effective characterization of minimal deadlocks and traps in Petri Nets based on graph theory Proc. of the 10h. Petri Net Conference on Theory and Applications of Petri Nets, Bonn, 1989Google Scholar
  3. [Bram83]
    BRAMS G.W., Réseaux de Petri. Theorie et Pratique (2 vol.), Masson, Paris, 1983Google Scholar
  4. [CoHP 91]
    COUVREUR J.M., HADDAD S., PEYRE J.F., Computation of Generative Families of Positive Semi-flows in Two Types of Colored Nets, 12h. Petri Net Conference on Theory and Applications of Petri Nets, Gerjn (Denmark), June 1991.Google Scholar
  5. [CoSi 89]
    COLOM J.M., SILVA M., Convex Geometry and Semiflows in P/T Nets. A comparative Study of Algorithms for Computation of Minimal p-Semiflows. 10th International Conference on Application and Theory of Petri Nets, Bonn, 1989.Google Scholar
  6. [Espa 89]
    ESPARZA J., Structure theory of Free Choice Nets, Ph. D. Thesis, Universidad de Zaragoza (Spain), 1989Google Scholar
  7. [EsSi 90]
    ESPARZA J., SILVA M., A polynomial-time algorithm to decide liveness of bounded free choice nets, To appear in Theoretical Computer Science.Google Scholar
  8. [EsSB 89]
    ESPARZA J., SILVA M., BEST E., Minimal deadlocks in Free Choice Nets, Hildesheimer Informatik Fachberichte 1/89, 1989Google Scholar
  9. [Hadd 87]
    HADDAD S., Une catégorie régulière de réseau de Petri de haut niveau: définition, propriétés et réductions. Application à la validation de systèmes distribués, Thèse de l'Université Pierre et Marie Curie, Paris, 1987Google Scholar
  10. [Laut 87]
    LAUTENBACH K., Linear Algebraic calculation of deadlocks and traps, Concurrency and nets, Voss-Genrich-Rozenberg eds., Springer Verlag,1987.Google Scholar
  11. [Memm 83]
    MEMMI G., Methode d'analyse de réseaux de Petri, réseaux à files, et applications au temps réel, Thèse de l'Université Pierre et Marie Curie, Paris, 1983.Google Scholar
  12. [MeVa87]
    MEMMI G., VAUTHERIN J., Analysing nets by the invariant method, Advances in Petri Nets 1986, L.N.C.S. 254, Springer-Verlag,1987.Google Scholar
  13. [MiBa 88a]
    MINOUX M., BARKAOUI K., Polynomial time algorithms for proving or disproving Commoner's structural property in Petri Nets, Proc. of the 9th. Petri Net Conference on Theory and Applications of Petri Nets, Venice, 1988Google Scholar
  14. [MiBa 88b]
    MINOUX M., BARKAOUI K., Polynomial algorithms for finding deadlocks, traps and other substructures relevant to Petri net analysis, Internal research report N. 212 of the Laboratoire MASI, Univ. Paris 6, Paris, 1988Google Scholar
  15. [Sifa 79]
    SIFAKIS J., Contrôle des systèmes asynchrones: concepts, proprietés, analyse statique, Thèse de l'Université Scientifique et Médical de Grenoble, 1979.Google Scholar
  16. [Silv 85]
    SILVA M., Las redes de Petri en la Informática y la Automática, Ed. AC, Madrid, 1985.Google Scholar
  17. [Toud 81]
    TOUDIC J.M., Algorithmes d'analyse structurelle de réseaux de Petri, Thèse de l'Université Pierre et Marie Curie, Paris, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • J. Ezpeleta
    • 1
  • J. M. Couvreur
    • 2
  • M. Silva
    • 3
  1. 1.Dpto. Ingeniería Eléctrica e InformáticaUniversidad de ZaragozaZaragozaSpain
  2. 2.Laboratoire MASIUniversité Paris VIParis Cedex 5France
  3. 3.Dpto. Ingeniería Eléctrica e InformáticaUniversidad de ZaragozaZaragozaSpain

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