Transition systems of Elementary Net Systems with inhibitor arcs

  • Marta Pietkiewicz-Koutny
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1248)


We here consider transition systems of Elementary Net Systems with inhibitor arcs. There are basically two different types of non-interleaving semantics of such Petri nets, the a-posteriori and a-priori semantics. The former is an instance of the causal partial order semantics, and can be captured using means similar to those developed for ordinary safe nets. The latter is based on an extension of the partial order semantics which includes weak causality in addition to the standard causality relationship. In this paper we deal only with the a-priori semantics. Our aim is to completely characterise transition systems which can be generated by Elementary Net Systems with inhibitor arcs. This is achieved by adapting the notion of a step transition system, i.e. one in which arcs are labelled by sets of events executed concurrently. In developing our model, we follow the standard approach in which the relationship between nets and their transition systems is established via the notion of a region. We define, and show consistency of, two behaviour preserving translations between nets and transition systems. Our results can be used to provide the basis for an automatic synthesis of nets with inhibitor arcs from operational descriptions expressed in terms of transition systems.


causality/partial order theory of concurrency analysis and synthesis structure and behaviour of nets 


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  1. 1.
    Bednarczyk M.A.: Categories of asynchronous systems. Ph.D. Thesis, University of Sussex (1988).Google Scholar
  2. 2.
    Billington J.: Extensions to coloured nets. Proc. of 3rd Int. Workshop on Petri Nets and Performance Models, Kyoto, Japan (1989), 61–70.Google Scholar
  3. 3.
    Bernardinello L., De Michelis G., Petruni K., Vigna S.: On the synchronie structure of transition systems. In: J. Desel (Ed.) Structures in Concurrency Theory, Berlin 1995, Workshops in Computing, Springer (1995), 69–84.Google Scholar
  4. 4.
    Chiola G., Donatelli S., Francheschinis G.: Priorities, inhibitor arcs and concurrency in P/T nets. Proc. of 12th Intern. Conf. on Appl. and Theory of Petri Nets, Gjern, Denmark (1991), 182–205.Google Scholar
  5. 5.
    Christiansen S., Hansen N.D.: Coloured Petri nets extended with place capacities, test arcs and inhibitor arcs. Proc. of Application and Theory of Petri Nets'93, Lecture Notes in Computer Science 651, Springer (1993), 186–205.Google Scholar
  6. 6.
    Hoogeboom H.J., Rozenberg G.: Diamond properties of elementary net systems. Fundamenta Informaticae XIV (1991), 287–300.Google Scholar
  7. 7.
    Janicki R., Koutny M.: Semantics of inhibitor nets. Information and Computation, Vol. 123, No. 1 (1995), 1–16.Google Scholar
  8. 8.
    Janicki R., Lauer P.E.: Specification and analysis of concurrent systems: the COSY approach. Springer-Verlag, (1992).Google Scholar
  9. 9.
    Keller R.M.: Formal verification of parallel programs. CACM, Vol. 19, No. 7 (1976), 371–389.Google Scholar
  10. 10.
    Montanari U., Rossi F.: Contextual nets. Acta Informatica 32 (1995), 545–596.Google Scholar
  11. 11.
    Mukund M.: Petri nets and step transition systems. International Journal of Foundations of Computer Science, Vol. 3, No. 4 (1992), 443–478.Google Scholar
  12. 12.
    Nielsen M., Rozenberg G., Thiagarajan P.S.: Elementary transition systems. Theoretical Computer Science 96 (1992), 3–33.Google Scholar
  13. 13.
    Shields M.W.: Concurrent machines. Computer Journal 28 (1985), 449–465.Google Scholar
  14. 14.
    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, Vol. 4 (1995), 1–148.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

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

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