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Acta Informatica

, Volume 44, Issue 7–8, pp 463–508 | Cite as

Recursive Petri nets

Theory and application to discrete event systems
  • Serge Haddad
  • Denis Poitrenaud
Original Article

Abstract

In order to design and analyse complex systems, modelers need formal models with two contradictory requirements: a high expressivity and the decidability of behavioural property checking. Here we present and develop the theory of such a model, the recursive Petri nets. First, we show that the mechanisms supported by recursive Petri nets enable to model patterns of discrete event systems related to the dynamic structure of processes. Furthermore, we prove that these patterns cannot be modelled by ordinary Petri nets. Then we study the decidability of some problems: reachability, finiteness and bisimulation. At last, we develop the concept of linear invariants for this kind of nets and we design efficient computations specifically tailored to take advantage of their structure.

Keywords

Label Transition System Discrete Event System Abstract Transition 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.

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References

  1. 1.
    Cassandras C.G. and Lafortune S. (1999). Introduction to Discrete Event Systems. Kluwer, Dordrecht MATHGoogle Scholar
  2. 2.
    Colom, J.M., Silva, M.: Convex geometry and semiflows in P/T nets. A comparative study of algorithms for computation of minimal P-semiflows. In: Advances in Petri Nets, volume 483 of Lecture Notes Computer Science, pp. 79–112. Springer, Heidelberg (1990)Google Scholar
  3. 3.
    Dufourd, C., Finkel, A., Schnoebelen, P.: Reset nets between decidability and undecidability. In: Proceedings of the 25th International Colloquium on Automata, Languages and Programming, volume 1443 of Lecture Notes Computer Science, pp. 103–115, Aalborg, Denmark, July 1998. Springer, Heidelberg (1998)Google Scholar
  4. 4.
    Eilenberg S. and Schütsenberger M.P. (1969). Rational sets in commutative monoïds. J. Algebra 13: 173–191 MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Esparza J. and Nielsen M. (1994). Decidability issues for Petri nets—a survey. Bull. Eur. Assoc. Theor. Comput. Sci. 52: 245–262 MATHGoogle Scholar
  6. 6.
    El Fallah Seghrouchni, A., Haddad, S.: A recursive model for distributed planning. In: Proceedings of the Second International Conference on Multi-Agent Systems, pp. 307–314, Kyoto, Japon, December 1996Google Scholar
  7. 7.
    Haddad, S., Poitrenaud, D.: Decidability and undecidability results for recursive Petri nets. Technical Report 019, LIP6, Paris VI University, Paris, France (1999)Google Scholar
  8. 8.
    Haddad, S., Poitrenaud, D.: Theoretical aspects of recursive Petri nets. In: Proceedings of the 20th International Conference on Applications and Theory of Petri nets, volume 1639 of Lecture Notes in Computer Science, pp. 228–247, Williamsburg, VA, USA. Springer, Heidelberg (1999)Google Scholar
  9. 9.
    Haddad, S., Poitrenaud, D.: Modelling and analyzing systems with recursive Petri nets. In: Proceedings of the 5th Workshop on Discrete Event Systems—Analysis and Control, pp. 449–458, Gand, Belgique, August 2000. Kluwer, Dordrecht (2000)Google Scholar
  10. 10.
    Haddad, S., Poitrenaud, D.: Checking linear temporal formulas on sequential recursive Petri nets. In: Proceedings of the 8th International Symposium on Temporal Representation and Reasonning, pp. 198–205, Cividale del Friuli, Italie. IEEE Computer Society Press (2001)Google Scholar
  11. 11.
    Jantzen M. (1979). On the hierarchy of Petri net languages. RAIRO 13(1): 19–30 MATHMathSciNetGoogle Scholar
  12. 12.
    Jančar P. (1995). Undecidability of bisimilarity for Petri nets and some related problems. Theor. Comput. Sci. 148: 281–301 CrossRefGoogle Scholar
  13. 13.
    Jančar P., Esparza J. and Moller F. (1999). Petri nets and regular processes. J. Comput. Syst. Sci. 59(3): 476–503 CrossRefGoogle Scholar
  14. 14.
    Jensen, K.: Coloured Petri nets. Basic concepts, analysis methods and practical use, vol. 1. Basic Concepts. Monographs in Theoretical Computer Science. Springer, Heidelberg (1997)Google Scholar
  15. 15.
    Kiehn, A.: Petri nets systems and their closure properties. In: Advances in Petri Nets 1989, volume 424 of Lecture Notes in Computer Science, pp. 306–328. Springer, Heidelberg (1989)Google Scholar
  16. 16.
    Köler, M., Rölke, H.: Properties of object Petri nets. In: Proceedings of the 25th International Conference on Application and Theory of Petri Nets, volume 3099 of Lecture Notes Computer Science, pp. 278–297, Bologna, Italy. Springer, Heidelberg (2004)Google Scholar
  17. 17.
    Kouchnarenko, O., Schnoebelen, Ph.: A model for recursive–parallel programs. In: Proceedings of the 1st International Workshop on Verification of Infinite State Systems, volume 5 of Electronic Notes in Theor. Comp. Sci., Pisa, Italy. Elsevier, Amsterdam (1997)Google Scholar
  18. 18.
    Kummer, O., Wienberg, F., Duvigneau, M., Schumacher, J., Köler, M., Moldt, D., Rölke, H., Valk, R.: An extensible editor and simulation engine for Petri nets: Renew. In: Proceedings of the 25th International Conference on Application and Theory of Petri Nets, volume 3099 of Lecture Notes Computer Science, pp. 484–493, Bologna, Italy, June 2004. Springer, Heidelberg (2004)Google Scholar
  19. 19.
    Lomazova, I., Schnoebelen, Ph.: Some decidability results for nested Petri nets. In: Proceedings of the 3rd International Andrei Ershov Memorial Conference Perspectives of System Informatics, volume 1755 of Lecture Notes Computer Science, pp. 208–220, Novosibirsk, Russia, July 2000. Springer, Heidelberg (2000)Google Scholar
  20. 20.
    Mayr, E.W.: An algorithm for the general Petri net reachability problem. In: Proceedings of the 13th Annual Symposium on Theory of Computing, pp. 238–246 (1981)Google Scholar
  21. 21.
    Mayr, R.: Combining Petri nets and PA-processes. In: Proceedings of the 3rd International Symposium on Theoretical Aspects of Computer Software, volume 1281 of Lecture Notes in Computer Science, pp. 547–561, Sendai, Japan, 1997. Springer, Heidelberg (1997)Google Scholar
  22. 22.
    Mayr R. (2000). Process rewrite systems. Inform. Comput. 156(1): 264–286 MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Rackoff C. (1978). The covering and boundedness problems for vector addition systems. Theor. Comput. Sci. 6: 223–231 MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Reutenauer C. (1990). The Mathematics of Petri Nets. Prentice-Hall, New York MATHGoogle Scholar
  25. 25.
    Sibertin-Blanc, C.: Cooperative objects: principles, use and implementation. In: Concurrent Object-Oriented Programming and Petri Nets, Advances in Petri Nets, volume 2001 of Lecture Notes Computer Science, pp. 216–246. Springer, Heidelberg (2001)Google Scholar
  26. 26.
    Valk, R.: On the computational power of extended Petri nets. In: Proceedings of the 7th International Symposium on Mathematical Foundations of Computer Science, volume 64 of Lecture Notes Computer Science, pp. 526–535, Zakopane, Poland. Springer, Heidelberg (1978)Google Scholar
  27. 27.
    Valk, R.: Self-modifying nets, a natural extension of Petri nets. In: Proceedings of the 5th International Colloquium on Automata, Languages and Programming, volume 62 of Lecture Notes Computer Science, pp. 464–476, Udine, Italy. Springer, Heidelberg (1978)Google Scholar
  28. 28.
    Valk, R.: Petri nets as token objects: An introduction to elementary object nets. In: Proceedings of the 19th International Conference on Application and Theory of Petri Nets, volume 1420 of Lecture Notes Computer Science, pp. 1–25. Springer, Heidelberg (1998)Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Université Paris-DauphineParis Cedex 16France
  2. 2.Université Paris VIParis Cedex 05France

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