Checking regular properties of Petri nets

  • Petr Jančar
  • Faron Moller
Session: Decidability Results
Part of the Lecture Notes in Computer Science book series (LNCS, volume 962)


In this paper we consider the problem of comparing an arbitrary Petri net against one whose places may contain only a bounded number of tokens (that is, against a regular behaviour), with respect to trace set inclusion and equivalence, as well as simulation and bisimulation. In contrast to the known result that language equivalence is undecidable, we find that all of the above are in fact decidable. We furthermore demonstrate that it is undecidable whether a given Petri net is either trace equivalent or simulation equivalent to any (unspecified) bounded net.


Regular Property Minsky Machine Simulation Expansion Trace Equivalent Decrement Action 
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]
    Abdulla, P., K. Čerāns, P. Jančar, and F. Moller. One counter Petri nets vs bounded Petri nets. Research Report, 1995.Google Scholar
  2. [2]
    Christensen, S., Y. Hirshfeld, and F. Moller. Bisimulation is decidable for basic parallel processes. In E. Best (editor), Proceedings of CONCUR'93: Concurrency Theory, Lecture Notes in Computer Science 715, pp143–157, Springer-Verlag, 1993.Google Scholar
  3. [3]
    Dickson, L.E. Finiteness of the odd perfect and primitive abundant numbers with distinct factors. American Journal of Mathematics 35, pp413–422, 1913.Google Scholar
  4. [4]
    Ginsburg, S., and E. Spanier. Semigroups, Presburger formulas, and languages. Pacific Journal of Mathematics 16, pp285–296, 1966.Google Scholar
  5. [5]
    van Glabbeek, R.J. The linear time — branching time spectrum. In J.C.M. Baeten, and J.W. Klop (editors), Proceedings of CONCUR'90: Concurrency Theory, Lecture Notes in Computer Science 458, pp278–297, Springer-Verlag, 1990.Google Scholar
  6. [6]
    Higman, H. Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society 3(2), pp326–336, 1952.Google Scholar
  7. [7]
    Hirshfeld, Y. Petri nets and the equivalence problem. In E. Börger, Y. Gurevich, and K. Meinke (editors), Proceedings of CSL'93: Computer Science Logic, Lecture Notes in Computer Science 832, pp165–174, Springer-Verlag, 1994.Google Scholar
  8. [8]
    Hopcroft, J.E., and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison Wesley, 1979.Google Scholar
  9. [9]
    Hüttel, H. Undecidable equivalences for basic parallel processes. In R.K. Shyamasundar (editor), Proceedings of FSTTCS'93: Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science 761, Springer-Verlag, 1993.Google Scholar
  10. [10]
    Jančar, P. Undecidability of bisimilarity for Petri nets and some related problems. Journal of Theoretical Computer Science (to appear). (A preliminary version appears in P. Enjalbert, E.W. Mayr and K.W. Wagner (editors), Proceedings of STACS'94: Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 775, pp581–592, Springer-Verlag, 1994.)Google Scholar
  11. [11]
    Jančar, P. Decidability questions for equivalences on Petri nets. Czech Habilitation Thesis. Masaryk University, Brno. (Submitted April 1995.)Google Scholar
  12. [12]
    Karp, R., and R. Miller. Parallel program schemata. Journal of Computer and System Sciences 3, pp167–195, 1969.Google Scholar
  13. [13]
    Mauw, S., and H. Mulder. Regularity of BPA-systems is decidable. In B. Jonsson and J. Parrow (editors), Proceedings of CONCUR'94: Concurrency Theory, Lecture Notes in Computer Science 836, pp34–47, Springer-Verlag, 1993.Google Scholar
  14. [14]
    Mayr, E. An algorithm for the general Petri net reachability problem. SIAM Journal of Computing 13, pp441–460, 1984.CrossRefGoogle Scholar
  15. [15]
    Mazurkiewicz, A. Trace theory. In W. Brauer, W. Reisig, and G. Rozenberg (editors), Petri Nets: Applications and Relationships to Other Models of Concurrency, Lecture Notes in Computer Science 255, pp279–324, Springer-Verlag, 1987.Google Scholar
  16. [16]
    Milner, R. Communication and Concurrency. Prentice Hall, 1989.Google Scholar
  17. [17]
    Minsky, M. Computation: Finite and Infinite Machines. Prentice Hall, 1967.Google Scholar
  18. [18]
    Peterson, J.L. Petri Net Theory and the Modeling of Systems. Prentice Hall, 1981.Google Scholar
  19. [19]
    Stirling, C. Local model checking games. Department of Computer Science Research Report, University of Edinburgh, 1995.Google Scholar
  20. [20]
    Valk, R., and G. Vidal-Naquet. Petri nets and regular languages. Journal of Computer and System Sciences 23(3), pp299–325, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Petr Jančar
    • 1
  • Faron Moller
    • 2
  1. 1.Department of Computer ScienceUniversity of OstravaOstrava 1Czech Republic
  2. 2.Swedish Institute of Computer ScienceKistaSweden

Personalised recommendations