Advertisement

Obtaining deadlock-preserving skeletons for coloured nets

  • Greg Findlow
Submitted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 616)

Abstract

We extend Vautherin's work on behavioural relationships between coloured nets and their skeletons, which are ordinary Petri nets. A desirable property for a coloured net to have is that a marking is dead if and only if the corresponding skeletal marking is dead. This guarantees that for each deadlock (i.e. reachable dead marking) of the coloured net, the corresponding skeletal marking is a deadlock, so coloured deadlocks are ‘preserved’ in the skeleton. Vautherin gave a rather restrictive sufficient condition for the aforementioned property. We formulate two necessary and sufficient conditions, thus identifying the class of coloured nets with ‘deadlockpreserving skeletons’. We then show how any coloured net may be ‘refolded’ to obtain one with the same behaviour as the original and with a deadlock-preserving skeleton. Consequently, all deadlocks of the original net may be detected via this skeleton. Moreover, the refolding transformation is optimal, in the sense that this skeleton is as small as possible.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Billington 89]
    J. Billington. Many-Sorted High-Level Nets. In Proceedings of the Third International Workshop on Petri Nets and Performance Models, Kyoto, Japan, 11–13 December 1989, pp. 166–179, IEEE CS Press, Washington, D.C., USA, 1989.Google Scholar
  2. [Chiola & 89]
    G. Chiola and G. Franceschini. Coloured GSPN models and automatic symmetry detection. In Proceedings of the Third International Workshop on Petri Nets and Performance Models, Kyoto, Japan, 11–13 December 1989, pp. 50–60, IEEE CS Press, Washington, D.C., USA, 1989.Google Scholar
  3. [Chiola & 91]
    G. Chiola and G. Franceschini. A Structural Colour Simplification in Well-Formed Coloured Nets. In Proceedings of the Fourth International Workshop on Petri Nets and Performance Models, Melbourne, Australia, 2–5 December 1991, pp.144–153, IEEE Computer Society Press 1991.Google Scholar
  4. [Ehrig & Mahr 85]
    H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1, Equations and Initial Semantics. Volume 6 of EATCS Monographs on Theoretical Computer Science, Springer-Verlag, Berlin, 1985.Google Scholar
  5. [Findlow 91]
    Greg Findlow. Can Skeletons Really Be Used to Detect Deadlocks of Nets? In Proceedings of the Fourth International Workshop on Petri Nets and Performance Models, Melbourne, Australia, 2–5 December 1991, pp. 198–203, IEEE Comp. Soc. Press 1991.Google Scholar
  6. [Findlow 92]
    G.A. Findlow. Using Skeletons for Deadlock Detection in TORAS. Draft AOTC Research Laboratories Report.Google Scholar
  7. [Huber & 85]
    P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen. Towards reachability trees for high-level Petri nets. In G. Rozenberg, ed., Advances in Petri Nets 1984. Lecture Notes in Computer Science, Vol. 188, pp. 215–233, Springer-Verlag, Berlin, 1985.Google Scholar
  8. [Huber & 91]
    P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen. Reachability Trees for High-level Petri Nets. In K. Jensen, G. Rozenberg, eds., High-level Petri Nets — Theory and Application, pp. 319–350, Springer-Verlag, Berlin, 1991.Google Scholar
  9. [Jensen 81]
    K. Jensen. Coloured Petri Nets and the invariant method. Theoretical Computer Science, 14: 317–336, 1981.CrossRefGoogle Scholar
  10. [Jensen 83]
    K. Jensen. High-level Petri Nets. Proc. of the 3rd European W'shop on App. and Theory of Petri Nets, Varenna, Italy, 1982. In A. Pagnoni and G. Rozenberg (eds.), Applications and Theory of Petri Nets, Inf.-Fachberichte Vol. 66, Springer-Verlag, 1983.Google Scholar
  11. [Jensen 87]
    K. Jensen. Coloured Petri Nets. In W. Brauer, W. Reisig, and G. Rozenberg (eds.), Petri Nets: Central Models and Their Properties, Advances in Petri Nets 1986, Part I. Lecture Notes in Comp. Science, Vol. 254, pp. 248–299, Springer-Verlag, Berlin, 1987.Google Scholar
  12. [Peterson 81]
    James L. Peterson. Petri Net Theory and the Modeling of Systems. Prentice Hall, Englewood Cliffs, N.J., 1981.Google Scholar
  13. [Reisig 85]
    Wolfgang Reisig. Petri Nets, An Introduction. Volume 4 of EATCS Monographs on Theoretical Computer Science, Springer-Verlag, Berlin, 1985.Google Scholar
  14. [Valmari 90]
    Antti Valmari. Stubborn Sets for Reduced State Space Generation. In G.Rozenberg, ed., Advances in Petri Nets 1990. Lecture Notes in Computer Science, Vol. 483, pp. 491–515, Springer-Verlag, Berlin, 1991.Google Scholar
  15. [Valmari 91]
    Antti Valmari. Stubborn Sets of Coloured Petri Nets. In Proceedings of the 12th International Conference on Application and Theory of Petri Nets, pp. 102–121, Gjern, Denmark, 26–28 June 1991.Google Scholar
  16. [Vautherin 87]
    J. Vautherin. Parallel systems specifications with Coloured Petri Nets and algebraic specifications. In G. Rozenberg, editor, Advances in Petri Nets 1987. Lecture Notes in Computer Science, Vol. 266, pp. 293–308, Springer-Verlag, Berlin, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Greg Findlow
    • 1
  1. 1.Telecommunications Research Laboratories of AOTCClaytonAustralia

Personalised recommendations