Advertisement

Semi-commutation and deterministic petri nets

  • Edward Ochmański
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 452)

Abstract

Semi-commutation rewriting systems have been introduced and investigated by Clerbout/Latteux [1]. Starting from those, the notions of semitraces, semi-commutative monoids and an order on those monoids are defined. Behaviours of Petri nets are represented by sets of semitraces. Using that tool, properties of Petri nets, mainly concerning determinism, are discussed. Deterministic Petri nets are characterized in terms of their configurations. The present approach is a generalization of the well-known Mazurkiewicz's [7] trace model.

Keywords

Concurrent System Firing Sequence Fireable Cycle Transition Capacity Concurrent State 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M.Clerbout/M.Latteux: Semi-Commutations; Information and Computation 73, 1987.Google Scholar
  2. [2]
    H.Genrich/E.Stankiewicz-Wiechno: A Dictionary of Some Basic Notions of Net Theory; LNCS 84, 1980.Google Scholar
  3. [3]
    U.Goltz/W.Reisig: The Non-Sequential Behaviour of Petri Nets; Information and Control 57, 1983.Google Scholar
  4. [4]
    U.Grude: Concurrency for P/T-Nets; Petri Net Newsletter 31, December 1988.Google Scholar
  5. [5]
    D.V.Hung/E.Knuth: Semi-Commutations and Petri Nets; Theoretical Computer Science 64.1, 1989.Google Scholar
  6. [6]
    A.Mazurkiewicz: Complete Processes and Inevitability; Report 86-06, University of Leiden 1986.Google Scholar
  7. [7]
    A.Mazurkiewicz: Trace Theory; Adv. Course on Petri Nets 86, LNCS 255, 1987.Google Scholar
  8. [8]
    A.Mazurkiewicz: Concurrency, Compositionality and Synchronization; Proc. of MFCS 89, LNCS 379, 1989.Google Scholar
  9. [9]
    A.Mazurkiewicz/E.Ochmanski/W.Penczek: Concurrent Systems and Inevitability; Theoretical Computer Science 64.3, 1989.Google Scholar
  10. [10]
    E.Ochmański: Semi-Commutation for Place/Transition Systems; Bulletin of EATCS 38, June 1989.Google Scholar
  11. [11]
    E.Ochmański/W.Penczek: Inevitability in Diamond Processes; Informatique Theorique et Applications 24.1, 1990.Google Scholar
  12. [12]
    G.Rozenberg: Behaviour of Elementary Net Systems; Adv. Course on Petri Nets 86, LNCS 254, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Edward Ochmański
    • 1
  1. 1.Institute of Computer Science Polish Academy of SciencesWarszawa

Personalised recommendations