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On questions of fairness and temporal logic for conflict-free Petri nets

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Advances in Petri Nets 1988 (APN 1987)

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

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Abstract

In this paper, we examine the complexity of the fair nontermination problem for conflict-free Petri nets under several definitions of fairness. For each definition of fairness, we are able to show the problem to be complete for either NP, PTIME, or NLOGSPACE. We then address the question of whether these results extend to the more general model checking problem with respect to the temporal logic for Petri nets introduced by Suzuki. Since many of the model checking problems concerning finite state systems can be reduced to a version of the fair nontermination problem, it would seem plausible that the model checking problem for conflict-free Petri nets would be decidable. However, it turns out that unless the logic is severely restricted, model checking is undecidable for conflict-free Petri nets. In particular, the problem is undecidable even when formulas are of the form Gf ("invariantly f") where f contains no temporal logic operators. On the other hand, we show that model checking for conflict-free Petri nets is NP-complete for L(F,X) — the logic restricted to the operators F (eventually), X (next time), ∧, and ∨, with negations allowed only on the predicates.

This work was supported in part by U.S. Office of Naval Research Grant No. N00014-86-K-0763 and National Science Foundation Grant No. CCR-8711579. A summary of the results was presented at the 8th European Workshop on Applications and Theory of Petri Nets.

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Authors and Affiliations

  1. Department of Computer Sciences, University of Texas at Austin, 78712-1188, Austin, Texas

    Rodney R. Howell & Louis E. Rosier

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  1. Rodney R. Howell
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  2. Louis E. Rosier
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Grzegorz Rozenberg

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© 1988 Springer-Verlag Berlin Heidelberg

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Howell, R.R., Rosier, L.E. (1988). On questions of fairness and temporal logic for conflict-free 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_30

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  • DOI: https://doi.org/10.1007/3-540-50580-6_30

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  • Print ISBN: 978-3-540-50580-8

  • Online ISBN: 978-3-540-46059-6

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