A polynomial-time graph algorithm to decide liveness of some basic classes of bounded Petri nets

  • Kamel Barkaoui
  • Michel Minoux
Submitted Papers

DOI: 10.1007/3-540-55676-1_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 616)
Cite this paper as:
Barkaoui K., Minoux M. (1992) A polynomial-time graph algorithm to decide liveness of some basic classes of bounded Petri nets. In: Jensen K. (eds) Application and Theory of Petri Nets 1992. ICATPN 1992. Lecture Notes in Computer Science, vol 616. Springer, Berlin, Heidelberg

Abstract

This paper is related to structural analysis of Petri nets where liveness and boundedness issues are addressed through the analysis of the combinatorial properties of the underlying graph. We first recall a number of basic results about liveness and boundedness involving combinatorial substructures (deadlocks and traps). It is then shown that testing whether a bounded Extended Free Choice net or a Non Self-Controlling net is structurally live can be reduced to the search for a strongly connected deadlock which is not a trap. This problem, in turn, is shown to be solvable in polynomial time through a purely combinatorial algorithm making combined use of Tarjan's strong connectivity algorithm and Minoux's LTUR algorithm for solving Horn satisfiability problems. Once structural liveness has been proved, testing liveness for a given initial marking is already known to be polynomially solvable.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Kamel Barkaoui
    • 1
  • Michel Minoux
    • 2
  1. 1.Laboratoire CEDRICConservatoire National des Arts et MétiersParisFrance
  2. 2.Laboratoire MASIUniversité Paris 6ParisFrance

Personalised recommendations