Skip to main content
SpringerLink
Log in

Reset nets between decidability and undecidability

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1443))

Included in the following conference series:

Abstract

We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decidability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separations between seemingly related problems. Our main theorem is the very surprising fact that boundedness is undecidable for Petri nets with Reset arcs.

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. P. A. Abdulla, K. čerāns, B. Jonsson, and T. Yih-Kuen. General decidability theorems for infinite-state systems. In Proc. 11th IEEE Symp. Logic in Computer Science (LICS'96), New Brunswick, NJ, USA, July 1996, pages 313–321, 1996.

    Google Scholar 

  2. T. Araki and T. Kasami. Some decision problems related to the reachability problem for Petri nets. Theoretical Computer Science, 3(1):85–104, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Billington. Extensions to coloured Petri nets and their applications to protocols. PhD thesis, University of Cambridge, UK, May 1991. Available as Tech. Report No.222.

    Google Scholar 

  4. G. Ciardo. Petri nets with marking-dependent arc cardinality: Properties and analysis. In Proc. 15th Int. Conf. Applications and Theory of Petri Nets, Zaragoza, Spain, June 1994, volume 815 of Lecture Notes in Computer Science, pages 179–198. Springer-Verlag, 1994.

    Google Scholar 

  5. A. Finkel. Reduction and covering of infinite reachability trees. Information and Computation, 89(2):144–179, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Finkel and Ph. Schnoebelen. Fundamental structures in well-structured infinite transition systems. In Proc. 3rd Latin American Theoretical Informatics Symposium (LATIN'98), Campinas, Brazil, Apr. 1998, volume 1380 of Lecture Notes in Computer Science. Springer-Verlag, 1998.

    Google Scholar 

  7. M. Hack. Decidability questions for Petri nets. PhD Thesis MIT/LCS/TR-161, Massachusetts Institute of Technology, Lab. for Computer Science, June 1976.

    Google Scholar 

  8. M. Kishinevsky, J. Cortadella, A. Kondratyev, L. Lavagno, A. Taubin, and A. Yakovlev. Coupling asynchrony and interrupts: Place chart nets. In Proc. 18th Int. Conf. Application and Theory of Petri Nets, Toulouse, France, June 1997, volume 1248 of Lecture Notes in Computer Science, pages 328–347. Springer-Verlag, 1997.

    Google Scholar 

  9. R. M. Karp and R. E. Miller. Parallel program schemata. Journal of Computer and System Sciences, 3(2):147–195, 1969.

    MATH  MathSciNet  Google Scholar 

  10. C. Lakos and S. Christensen. A general approach to arc extensions for coloured Petri nets. In Proc. 15th Int. Conf. Applications and Theory of Petri Nets, Zaragoza, Spain, June 1994, volume 815 of Lecture Notes in Computer Science, pages 338–357. Springer-Verlag, 1994.

    Google Scholar 

  11. J. L. Peterson. Petri Net Theory and the Modeling of Systems. Prentice Hall Int., 1981.

    Google Scholar 

  12. C. Rackoff. The covering and boundedness problems for vector addition systems. Theoretical Computer Science, 6(2):223–231, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  13. K. Reinhardt. Reachability in Petri nets with inhibitor arcs, November 1995. Unpublished manuscript. See www-fs.informatik.uni-tuebingen.de/~reinhard.

    Google Scholar 

  14. R. Valk. On the computational power of extended Petri nets. In Proc. 7th Symp. Math. Found. Comp. Sci. (MFCS'78), Zakopane, Poland, Sep. 1978, volume 64 of Lecture Notes in Computer Science, pages 526–535, 1978.

    Google Scholar 

  15. R. Valk. Self-modifying nets, a natural extension of Petri nets. In Proc. 5th Int. Coll. Automata, Languages, and Programming (ICALP'78), Udine, Italy, Jul. 1978, volume 62 of Lecture Notes in Computer Science, pages 464–476. Springer-Verlag, 1978.

    Google Scholar 

  16. W. Vogler. Partial order semantics and read arcs. In Proc. 22nd Int. Symp. Math. Found. Comp. Sci. (MFCS'97), Bratislava, Slovakia, Aug. 1997, volume 1295 of Lecture Notes in Computer Science, pages 508–517. Springer-Verlag, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lab. Specification and Verification, ENS de Cachan & CNRS URA 2236, 61, av. Pdt Wilson, 94235, Cachan Cedex, France

    C. Dufourd, A. Finkel & Ph. Schnoebelen

Authors
  1. C. Dufourd
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Finkel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ph. Schnoebelen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Kim G. Larsen Sven Skyum Glynn Winskel

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dufourd, C., Finkel, A., Schnoebelen, P. (1998). Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055044

Download citation

  • DOI: https://doi.org/10.1007/BFb0055044

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64781-2

  • Online ISBN: 978-3-540-68681-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation