About the concurrent behaviour of EN systems: Definability and closure results

  • Elisabeth Pelz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 424)


We investigate the concurrent behaviour of elementary net systems in terms of partial word languages. We obtain its definability by existential sentences of the monadic second order logic. The class of these languages of λ-free labeled EN systems is closed under conjunction, disjunction and projection but not under complementation. This implies that existential sentences of the considered logic do not necessarly define the behaviour of these EN systems. A similar study is made for unlabeled EN systems, too.

Key words

Elementary net systems concurrent behaviour partial word languages definability monadic second order logic logical specifications 


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  1. [Bra,Rei,Roz]
    W. BRAUER, W. REISIG, G. ROZENBERG, editors, Petri Nets: Central Models and Their Properties, part 1, and, Petri Nets: Applications and Relationships to Other Models, part 2, Proceedings, Advances in petri nets 1986, LNCS 254 and 255, Springer-Verlag (1987)Google Scholar
  2. [Bue]
    J.R. BÜCHI, Weak second-order arithmetic and finite automata, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 6 (1960)Google Scholar
  3. [Grab]
    J. GRABOWSKI, On partial languages, Annales Soc. Math. Polonae, series IV: Fundamenta Informaticae IV.2 (1981)Google Scholar
  4. [Grau]
    P. GRAUBMANN, Construction of EN systems with a given trace behaviour, in Proceedings of the 8th European Workshop ... of Petri Nets, Zaragoza, 1987Google Scholar
  5. [Hac]
    M. HACK, Petri net languages, MIT — Technical report 159, (1975)Google Scholar
  6. [Jan]
    M. JANTZEN, Language theory of Petri nets, in [Bra,Rei,Roz]Google Scholar
  7. [Kie]
    A. KIEHN, On the concurrent behaviour of Petri nets, Universität Hamburg, Informatik-Bericht Nr. 120, (1986)Google Scholar
  8. [Och]
    E. OCHMANSKI, Occurrence traces — Processes of elementary net systems, in Proceedings of the 8th European Workshop ... of Petri Nets, Zaragoza, 1987Google Scholar
  9. [Par,Pel]
    M. PARIGOT, E. PELZ, A logical approach of Petri net languages, TCS 39 (1985)Google Scholar
  10. [Pel]
    E. PELZ, Infinitary languages of Petri nets and logical sentences, Advances in Petri nets 1987, LNCS 266, ed. by G. Rozenberg, Springer-Verlag (1987)Google Scholar
  11. [Pet]
    J.L. PETERSON, Petri net theory and the modeling of systems, Prentice-Hall, (1981)Google Scholar
  12. [Sta]
    P. STARKE, Processes in Petri nets, in Fundamentals of Computation theory, LNCS 117, ed. by F. Gécseg, Springer-Verlag (1981) also as full version: Elektronische Informationsverarbeitung und Kybernetik EIK 17, 8/9, (1981)Google Scholar
  13. [Roz]
    G. ROZENBERG, Behaviour of elementary net systems, in [Bra,Rei,Roz]Google Scholar
  14. [Thi]
    P.S. THIAGARAJAN, Elementary net systems, in [Bra,Rei,Roz]Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Elisabeth Pelz
    • 1
  1. 1.LRI, CNRS U.A. 410Université Paris Sud, Bât. 490Orsay CedexFrance

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