Advertisement

Testing Undecidability of the Reachability in Petri Nets with the Help of 10th Hilbert Problem

  • Piotr Chrząstowski-Wachtel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1639)

Abstract

The 10th Hilbert problem is used as a test for undecidability of reachability problem in some classes of Petri Nets, such as self-modifying nets, nets with priorities and nets with inhibitor arcs. Common method is proposed in which implementing in a weak sense the multiplication in a given class of Petri nets including PT-nets is sufficient for such undecidability.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. DFSch 98.
    C. Dufourd, A. Finkel, Ph. Schnoebelen, Reset nets: between decidability and undecidability, Proceedings ICALP 98, Aalborg (1998)Google Scholar
  2. Hack 74.
    M. Hack, Decidability question for Petri nets, PhD thesis, Department of Electrical Engineering, MIT 1974.Google Scholar
  3. Hack 76.
    M. Hack, The equality problem for vector addition systems is undecidable, Th. Comp. Sc. 1976, 2, pp 77–95 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  4. Kindler 98.
    E. Kindler, Private communication.Google Scholar
  5. Kosaraju 82.
    S.R. Kosaraju, Decidability of Reachability in Vector Addition Systems, In Proc. of the 14th Annual ACM Symp. on Theory of Computing, San Francisco, May 5-7, 1982, pages 267–281 (1982)Google Scholar
  6. Matijasevich 70.
    Y. Matijasevich, Enumerable sets are Diophantine(in Russian), Dokl. Akad. Nauk SSSR, 191, pp 279–282 (1970). Translation in: Soviet Math. Doklady, 12 pp 249-254, (1971)Google Scholar
  7. Mayr 81.
    E. Mayr, An algorithm for the general Petri net reachability problem. Proceedings of the 13th Ann. ACM Symposium on Theory of Computing, May 11-13, 1981 (Milwaukee, WI), pp. 238–246. Also: SIAM Journal on Computing 13, 3, pp. 441-460.Google Scholar
  8. Tarlecki 83.
    A. Tarlecki, An obvious observation on functions computable by Petri Nets, SIG Petri Nets and Related Models, Newsletter 13 (February 1983)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Piotr Chrząstowski-Wachtel
    • 1
  1. 1.Institute of InformaticsWarsaw UniversityWarszawaPoland

Personalised recommendations