Skip to main content
SpringerLink
Log in

Some consequences of the decidability of the reachability problem for Petri nets

  • Conference paper
  • First Online:
Book cover Advances in Petri Nets 1988 (APN 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 340))

Included in the following conference series:

Abstract

The aim of this article is to explain and elucidate Mayr's and Kosaraju's proof of the decidability of reachability in Petri nets. We introduce the new notion of precovering graphs which allows to suppress technical steps and makes the result clearer. We obtain a new structure on Petri nets: the perfect marked graph-transition sequences which generalises, in the case we add a final marking to the Petri net, the covering graph. We deduce from this structure new results in Petri net language theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Dershowitz, Z. Manna, Proving termination with multiset ordering, Comm. ACM, August 79, Volume 22, Nr 8.

    Google Scholar 

  2. J.Hopcroft, J.J. Pansiot, On the reachability problem for 5-dimensional vector addition systems, Theoret. Comp. Sci., 1978, 135–159.

    Google Scholar 

  3. M. Jantzen, On the hierarchy of Petri net languages, RAIRO Vol 13 no1, 1979, 19–30.

    Google Scholar 

  4. R.M. Karp, R.E. Miller, Parallel program schemata, J. Comput. Sci. 3 (May 1969) 147–195.

    Google Scholar 

  5. S.R. Kosaraju, Decidability of reachability in vector addition systems, Proc. 14 th ann. ACM STOC, 1982, 267–281.

    Google Scholar 

  6. J.L. Lambert, A structure to decide reachability in Petri net, to appear in Theoret. Comp. Sci.

    Google Scholar 

  7. J.L. Lambert, Finding a partial solution to a linear system of equations in positive integer, Comput. Math. Applic. Vol. 15, No3, pp 209–212, 1988.

    Google Scholar 

  8. E. Mayr, An algorithm for the general Petri net reachability problem, SIAM, J. Comput., Vol 13 No3, 1984, 441–460. And

    Google Scholar 

  9. E.Mayr, An algorithm for the general Petri net reachability problem, Proc. 13 th ann. ACM STOC, 1981, 238–246.

    Google Scholar 

  10. H. Muller, The reachability problem for VAS, Advances in Petri nets 1984, LNCS 188, 376–391

    Google Scholar 

  11. M. Parigot, E. Pelz, A logical formalism for the study of the finite behaviour of Petri nets, Advances in Petri net 1985, LNCS 222, 346–361

    Google Scholar 

  12. C.A. Petri, Kommunikation mit Automaten, Institut für Instrumentelle Mathematik (Bonn), Schriften des IMM Nr 2, 1962.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de recherche en informatique CNRS UA 410, Université de Paris-Sud Centre d'Orsay, Bat 490, 91405, Orsay, France

    J. L. Lambert

Authors
  1. J. L. Lambert
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lambert, J.L. (1988). Some consequences of the decidability of the reachability problem for Petri nets. In: Rozenberg, G. (eds) Advances in Petri Nets 1988. APN 1987. Lecture Notes in Computer Science, vol 340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50580-6_33

Download citation

  • DOI: https://doi.org/10.1007/3-540-50580-6_33

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50580-8

  • Online ISBN: 978-3-540-46059-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation