Region Based Synthesis of P/T-Nets and Its Potential Applications

  • Philippe Darondeau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1825)

Abstract

This talk is an informal presentation of ideas put forward by Badouel, Bernardinello, Caillaud and me for solving various types of P/T-net synthesis problems, with hints at the potential role of net synthesis in distributed software and distributed control. The ideas are theirs as much as mine. The lead is to start from Ehrenfeucht and Rozenberg’s axiomatic characterization of behaviours of elementary nets, based on regions, to adapt the characterization to P/T-nets in line with Mukund’s extended regions with integer values, and to profit from algebraic properties of graphs and languages for converting decision problems about regions to linear algebra.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chernikova, N.V.: Algorithm for finding a general formula for the non-negative solutions of a system of linear inequalities. U.S.S.R. Computational Math. and Math. Physics 5 no.2 (1965) 228–233MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Arnold, A., Nivat, M.: Comportements de processus. Les mathématiques de l’informatique, colloque AFCET (1982) 35–68Google Scholar
  3. 3.
    Ehrenfeucht, A., Rozenberg, G.: Partial (Set) 2-Structures; part I: Basic Notions and the Representation Problem. Acta Informatica 27 (1990) 315–342MATHMathSciNetGoogle Scholar
  4. 4.
    Ehrenfeucht, A., Rozenberg, G.: Partial (Set) 2-Structures; part II: State Spaces of Concurrent Systems. Acta Informatica 27 (1990) 343–368MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Mukund, M.: Petri Nets and Step Transition Systems. Int. Journal of Found. of Comp. Science 3 no.4 (1992) 443–478MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Rudie, K., Wonham, W.M.: Think Globally, Act Locally: Decentralized Supervisory Control. IEEE Trans. on Automatic Control 37 no.11 (1992) 1692–1707MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Droste, M., Shortt, R.M.: Petri Nets and Automata with Concurrency Relations-an Adjunction. Semantics of Programming Languages and Model Theory, M. Droste and Y. Gurevich eds (1993) 69–87Google Scholar
  8. 8.
    Badouel, E., Bernardinello, L., Darondeau, Ph.: Polynomial algorithms for the synthesis of bounded nets. Proc. CAAP, LNCS 915 (1995) 364–378Google Scholar
  9. 9.
    Jancar, P., Moeller, F.: Checking Regular Properties of Petri Nets, Proc. Concur, LNCS 962 (1995) 348–362Google Scholar
  10. 10.
    Badouel, E., Darondeau, Ph.: Dualities between nets and automata induced by schizophrenic objects. Proc. CTCS, LNCS 953 (1995) 24–43Google Scholar
  11. 11.
    Desel, J., Reisig, W.: The Synthesis Problem of Petri Nets. Acta Informatica 33 (1996) 297–315CrossRefMathSciNetGoogle Scholar
  12. 12.
    Badouel, E., Darondeau, Ph.: Theory of regions. Lectures on Petri Nets I: Basic Models, LNCS 1491 (1998) 529–586Google Scholar
  13. 13.
    Bernardinello, L.: Propriétés algébriques et combinatoires des régions dans les graphes et leur application à la synthèse de réseaux. Thèse, Univ. Rennes (1998)Google Scholar
  14. 14.
    Darondeau, Ph.: Deriving Unbounded Petri Nets from Formal Languages. Proc. Concur, LNCS 1466 (1998) 533–548Google Scholar
  15. 15.
    Badouel, E.: Automates réversibles et réseaux de Petri, dualité et représentation: le problème de synthèse. Document d’habilitation 31, Irisa (1999) available from http://www.irisa.fr/EXTERNE/bibli/habilitations.html
  16. 16.
    Caillaud, B.: Bounded Petri-net Synthesis Techniques and their Applications to the Distribution of Reactive Automata. JESA 9–10 no.33 (to appear)Google Scholar
  17. 17.
    Darondeau, Ph.: On the Petri Net Realization of Context-Free Graphs. (to appear)Google Scholar
  18. 18.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Philippe Darondeau
    • 1
  1. 1.IRISARennes Cedex

Personalised recommendations