Synthesis of ENI-systems using minimal regions

  • Marta Pietkiewicz-Koutny
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1466)


We consider the synthesis problem for Elementary Net Systems with Inhibitor Arcs (ENI-systems) executed according to the a-priori semantics. The relationship between nets and transition systems generate by them (TSENI) is established via the notion of a region. The general synthesis problem for ENI-systems was solved in [20], and here we show how to optimise this solution using only minimal regions and selected inhibitor arcs. We also compare the proposed method of eliminating inhibitor arcs in ENI-systems with that introduced in [8] and show that they have similar effect.


Petri nets concurrency transition systems regions synthesis of nets 


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  1. 1.
    Arnold A.: Finite transition systems. Prentice Hall International (1994).Google Scholar
  2. 2.
    Badouel E., Bernardinello L., Darondeau Ph.: Polynomial algorithms for the synthesis of bounded nets. Proc. of CAAP'95, P.D. Mosses, M. Nielsen, M.I. Schwartzbach (Eds.), Springer-Verlag, LNCS 915 (1995), 364–378.Google Scholar
  3. 3.
    Badouel E., Bernardinello L., Darondeau Ph.: The synthesis problem for elementary net systems is NP-complete. Theoretical Computer Science 186 (1997), 107–134.MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Badouel E., Darondeau Ph.: Theory of regions. Third Advanced Course on Petri Nets, Springer-Verlag, LNCS (1997), to appear.Google Scholar
  5. 5.
    Billington J.: Extensions to coloured Petri nets. Proc. of 3rd Int. Workshop on Petri Nets and Performance Models, Kyoto, Japan (1989), 61–70.Google Scholar
  6. 6.
    Bernardinello L.: Synthesis of net systems. Proc. of ICATPN'93, M. Ajmone Marsan (Ed.), Springer-Verlag, LNCS 691 (1993), 89–105.Google Scholar
  7. 7.
    Bernardinello L., De Michelis G., Petruni K., Vigna S.: On the synchronic structure of transition systems. In: J.Desel (Ed.) Structures in Concurrency Theory, Berlin 1995, Workshops in Computing, Springer-Verlag (1995), 69–84.Google Scholar
  8. 8.
    Busi N., Pinna G.M.: Synthesis of nets with inhibitor arcs. Proc. of CONCUR'97, A. Mazurkiewicz and J. Winkowski (Eds.), Springer-Verlag, LNCS 1243 (1997), 151–165.Google Scholar
  9. 9.
    Chiola G., Donatelli S., Franceschinis G.: Priorities, inhibitor arcs, and concurrency in P/T nets. Proc. of ICATPN'91, Gjern, Denmark (1991), 182–205.Google Scholar
  10. 10.
    Christiansen S., Hansen N.D.: Coloured Petri nets extended with place capacities, test arcs and inhibitor arcs. Proc. of ICATPN'93, M. Ajmone Marsan (Ed.), Springer-Verlag, LNCS 691 (1993), 186–205.Google Scholar
  11. 11.
    Cortadella J., Kishinevsky M., Lavagno L., Yakovlev A.: Synthesizing Petri nets from state-based models. Proc. of ICCAD'95 (1995), 164–171.Google Scholar
  12. 12.
    Desel J., Reisig W.: The synthesis problem of Petri nets. Acta Informatica 33 (1996), 297–315.MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Ehrenfeucht A., Rozenberg G.: Partial 2-structures; Part I: Basic notions and the representation problem, and Part II: State spaces of concurrent systems. Acta Informatica 27 (1990), 315–368.MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Hoogeboom H.J., Rozenberg G.: Diamond properties of elementary net systems. Fundamenta Informaticae XIV (1991), 287–300.MathSciNetGoogle Scholar
  15. 15.
    Janicki R., Koutny M.: Semantics of inhibitor nets. Information and Computation 123 (1995), 1–16.MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Keller R.M.: Formal verification of parallel programs. CACM 19 (1976), 371–389.MATHGoogle Scholar
  17. 17.
    Montanari U., Rossi F.: Contextual nets. Acta Informatica 32 (1995), 545–596.MATHMathSciNetGoogle Scholar
  18. 18.
    Mukund M.: Petri nets and step transition systems. International Journal of Foundations of Computer Science 3 (1992), 443–478.MATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    Nielsen M., Rozenberg G., Thiagarajan P.S.: Elementary transition systems. Theoretical Computer Science 96 (1992), 3–33.MATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Pietkiewicz-Koutny M.: Transition systems of elementary net systems with inhibitor arcs. Proc. of ICATPN'97, P. Azema and G. Balbo (Eds.), Springer-Verlag, Lecture Notes in Computer Science 1248 (1997), 310–327.Google Scholar
  21. 21.
    Pietkiewicz-Koutny M.: Morphisms for inhibitor nets and related transition systems. Technical Report 613, Department of Computing Science, University of Newcastle upon Tyne, (1997).Google Scholar
  22. 22.
    Winskel G., Nielsen M.: Models for concurrency. In: S.Abramsky, Dov M.Gabbay and T.S.E.Maibaum (Eds.), Handbook of Logic in Computer Science 4 (1995), 1–148.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Marta Pietkiewicz-Koutny
    • 1
  1. 1.Department of Computing ScienceUniversity of Newcastle upon TyneNewcastle upon TyneUK

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