Reducing k-Safe Petri Nets to Pomset-Equivalent 1-Safe Petri Nets

  • Eike Best
  • Harro Wimmel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1825)


It is a well-known fact that for every k-safe Petri net, i.e. a Petri net in which no place contains more than k ∈ ℕ tokens under any reachable marking, there is a 1-safe Petri net with the same interleaving behaviour. Indeed these types of Petri nets generate regular languages. In this paper, we show that this equivalence of k-safe and 1-safe Petri nets holds also for their pomset languages, a true-concurrency semantics.


Causality / partial order theory of concurrency Petri nets Pomsets 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Bes84]
    E. Best: In Quest of a Morphism. Petri Net Newsletters Vol. 18, pp.14–18, 1984.MathSciNetGoogle Scholar
  2. [EHK96]
    T. Emden-Weinert, S. Hougardy, B. Kreuter, H.J. Prömel, A. Steger: Einführung in Graphen und Algorithmen. Skriptum der Humboldt-Universität Berlin, 1996.Google Scholar
  3. [GV83]
    U. Goltz, U. Vogt: Processes of Relation Nets. Petri Net Newsletters Vol. 14, pp.10–19, 1983.Google Scholar
  4. [GR83]
    U. Goltz, W. Reisig: The Non-sequential Behaviour of Petri Nets. Information and Control Vol. 57, pp.125–147, 1983.MATHCrossRefMathSciNetGoogle Scholar
  5. [Gra81]
    J. Grabowski: On Partial Languages. Annales Societatis Mathematicae Polonae, Fundamenta Informaticae Vol. IV.2, pp.428–498, 1981.Google Scholar
  6. [Jen92]
    K. Jensen: Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use. Volume 1. EATCS Monographs on Theoretical Computer Science, Springer-Verlag, 1992.Google Scholar
  7. [Pe92]
    E. Pelz: Normalization of Place/Transition Systems Preserves Net Behaviour. Informatique Théorique et Applications Vol. 26/1, pp.19–44, 1992.MATHMathSciNetGoogle Scholar
  8. [PRS92]
    L. Pomello, G. Rozenberg, C. Simone: A Survey of Equivalence Notions for Net Based Systems. Lecture Notes in Computer Science Vol. 609, pp.410–472, 1992.Google Scholar
  9. [Pra84]
    V. Pratt: Modeling Concurrency with Partial Orders. International Journal of Parallel Processing no. 15, pp.33–71, 1986.MATHCrossRefMathSciNetGoogle Scholar
  10. [PW97]
    L. Priese, H. Wimmel: Algebraic Characterization of Petri Net Pomset Languages. Proceedings of CONCUR’97, Lecture Notes in Computer Science Vol. 1243, pp.406–420, 1997.Google Scholar
  11. [PW98]
    L. Priese, H. Wimmel: A Uniform Approach to True-Concurrency and Interleaving Semantics for Petri Nets. Theoretical Computer Science Vol. 206, pp.219–256, 1998.MATHCrossRefMathSciNetGoogle Scholar
  12. [Rei98]
    W. Reisig: Elements of Distributed Algorithms. Springer-Verlag, 1998.Google Scholar
  13. [Smi98]
    E. Smith: Principles of High-level Net Theory. in: Lectures on Petri Nets I, Basic Models, Lecture Notes in Computer Science Vol. 1491, pp.174–210, 1998.Google Scholar
  14. [Tve67]
    H. Tverberg: On Dilworth’s Decomposition Theorem for Partially Ordered Sets. J. of Combin. Theory Vol. 3, pp.305–306, 1967.MATHCrossRefMathSciNetGoogle Scholar
  15. [Wim00]
    H. Wimmel: Algebraische Semantiken für Petri-Netze. Ph.D. Thesis, Universität Koblenz-Landau, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Eike Best
    • 1
  • Harro Wimmel
    • 2
  1. 1.Carl von Ossietzky Universität OldenburgOldenburg
  2. 2.Universität Koblenz-LandauKoblenz

Personalised recommendations