Behaviour preserving refinements of Petri nets

  • Walter Vogler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 246)


In a hierarchic design of a Petri net a host net, which is a ”rough” model, is refined by replacing a transition by a daughter net, that simulates the transition. For the independent design of host and daughter net those daughter nets are of interest that guarantee that an arbitrary host has the same behaviour as the respective refined net. We characterize these daughter nets, called modules, prove that it is decidable whether a net is a module and show how firing sequences and reachable markings of module, host and refined net are interrelated. Our results shed some light on the problem what a homomorphism of Petri nets should be and allow the generation of live Petri nets.


Bounded Module Input Place Firing Sequence Output Place Hierarchic Design 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    C. André: Use of the behaviour equivalence in place-transition net analysis. In: Girault/Reisig (ed.): Application and theory of Petri nets. Informatik Fachberichte 52, Springer 1982, p. 241–250Google Scholar
  2. [2]
    C. André: Structural transformations giving B-equivalent PT-nets. In: Pagnoni/Rosenberg (ed.): Application and theory of Petri nets. Informatik Fachberichte 66, Springer 1983, p. 14–28Google Scholar
  3. [3]
    C. André: The behaviour of a Petri net on a subset of transitions. RAIRO Autom. 17, 1983, p. 5–21Google Scholar
  4. [4]
    G. Berthelot: Transformations of Petri nets. Proc. 5th European workshop on appl. and theory of Petri nets, Aarhus, 1984, p. 310–328Google Scholar
  5. [5]
    H.J. Genrich, E. Stankiewicz-Wichno: A dictionary of some basic notions of net theory. In: W. Brauer (ed.): Net theory and applications, LNCS 84 (1980), p. 519–531Google Scholar
  6. [6]
    A. Habel, H.-J. Kreowski: Some structural aspects of hypergraph languages generated by hyperedge replacement. Techn. Report Nr. 12, TU Berlin, 1985.Google Scholar
  7. [7]
    L. Pomello: Some equivalence notions for concurrent systems. An overview. In: G.Rozenberg (ed.): Advances in Petri nets 1985, LNCS 222 (1986), p. 381–400Google Scholar
  8. [8]
    I. Suzuki, T. Murata: A method for stepwise refinement and abstraction of Petri nets. J. Comp. Syst. Sciences 27, 1983, p. 51–76CrossRefGoogle Scholar
  9. [9]
    R. Valette: Analysis of Petri nets by stepwise refinements. J. Comp. Syst. Sciences 18, 1979, 35–46CrossRefGoogle Scholar
  10. [10]
    K. Voss: A predicate/transition-net model of a local area network protocol. Proc. 5th European workshop on appl. and theory of Petri nets, Aarhus, 1984, p. 290–309Google Scholar
  11. [11]
    G. Winskel: A new definition of morphisms on Petri nets. Proc. STACS, Paris 1984, LNCS 166, p. 140–150Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Walter Vogler
    • 1
  1. 1.Institut für Informatik TU MünchenGermany

Personalised recommendations