Skip to main content
SpringerLink
Log in

Shortest paths in reachability graphs

  • Full Papers
  • Conference paper
  • First Online:
Book cover Application and Theory of Petri Nets 1993 (ICATPN 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 691))

Included in the following conference series:

Abstract

We prove the following property for safe conflict-free Petri nets and live and safe extended free-choice Petri nets:

Given two markings M 1 , M 2 of the reachability graph, if some path leads from M 1 to M 2, then some path of polynomial length in the number of transitions of the net leads from M 1 to M 2.

Work partly done within the Esprit Basic Research WG 6067: CALIBAN and within SFB 342, WG A3: SEMAFOR.

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. T. van Aardenne-Ehrenfest and N.G. de Bruijn: Circuits and Trees in Oriented Linear Graphs, Simon Stevin 28, 203–217 (1951).

    Google Scholar 

  2. E. Best and J. Desel: Partial Order Behaviour and Structure of Petri Nets. Formal Aspects of Computing Vol. 2 No.2, 123–138 (1990).

    Google Scholar 

  3. E. Best and J. Esparza: Model Checking of Persistent Petri Nets. Computer Science Logic 91, E. Börger, G. Jäger, H. Kleine Büning and M.M. Richter (eds.), LNCS 626, 35–53 (1992).

    Google Scholar 

  4. E. Best and P.S. Thiagarajan: Some Classes of Live and Save Petri Nets. Concurrency, K. and Nets K., Voss H.J., Genrich G., Rozenberg G. (eds.), Advances in Petri Nets. — Berlin: Springer-Verlag, 71–94 (1987).

    Google Scholar 

  5. E. Best and K. Voss: Free Choice Systems have Home States. Acta Informatica 21, 89–100 (1984).

    Google Scholar 

  6. F. Commoner, A.W. Holt, S. Even and A. Pnueli: Marked Directed Graphs. Journal of Computer and System Science Vol. 5, 511–523 (1971).

    Google Scholar 

  7. J. Esparza: Model Checking Using net Unfoldings. Hildesheimer Informatik Fachbericht 14/92 (October 1992). To appear in the Proceedings of TAPSOFT'93.

    Google Scholar 

  8. H. Fleischner: Eulerian Graphs and Related Topics, Part 1, Volume 1. Annals of Discrete Mathematics Vol.45. North-Holland (1990).

    Google Scholar 

  9. H.J. Genrich and K. Lautenbach: Synchronisationsgraphen. Acta Informatica Vol. 2, 143–161 (1973).

    Google Scholar 

  10. M. Hack: Analysis of Production Schemata by Petri Nets. TR-94, MIT-MAC (1972). Corrections (1974).

    Google Scholar 

  11. R. Howell and L. Rosier: On questions of fairness and temporal logic for conflict-free Petri nets. Advances in Petri Nets 1988, G. Rozenberg (ed.), LNCS 340, 200–226 (1988).

    Google Scholar 

  12. L. Landweber and E. Robertson: Properties of Conflict-Free and Persistent Petri Nets. JACM, Vol. 25, No.3, 352–364 (1978).

    Google Scholar 

  13. K.L. McMillan: Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. Proceedings of the 4th Workshop on Computer Aided Verification, Montreal, pp. 164–174 (1992).

    Google Scholar 

  14. P.S. Thiagarajan and K. Voss: A Fresh look at free-choice Nets. Information and Control, Vol. 61, No. 2, 85–113 (1984).

    Google Scholar 

  15. H. Yen: A polynomial time algorithm to decide pairwise concurrency of transitions for 1-bounded conflict-free Petri nets. Information Processing Letters 38, 71–76 (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Arcisstraße 21, D-8000, München 2

    Jörg Desel

  2. Institut für Informatik, Universität Hildesheim, Samelsonplatz 1, D-3200, Hildesheim

    Javier Esparza

Authors
  1. Jörg Desel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Javier Esparza
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Marco Ajmone Marsan

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Desel, J., Esparza, J. (1993). Shortest paths in reachability graphs. In: Ajmone Marsan, M. (eds) Application and Theory of Petri Nets 1993. ICATPN 1993. Lecture Notes in Computer Science, vol 691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56863-8_49

Download citation

  • DOI: https://doi.org/10.1007/3-540-56863-8_49

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56863-6

  • Online ISBN: 978-3-540-47759-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation