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Proving non-reachability by modulo-place-invariants

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Foundation of Software Technology and Theoretical Computer Science (FSTTCS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 880))

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Abstract

The reachability problem of Petri nets is the problem of deciding whether a marking can be reached from the initial marking by a sequence of occurrences of transitions. It is decidable in general, but it has a very high complexity.

For proving that a given marking is not reachable, the technique of invariants can be used. The best known and most applied invariant properties are those derived from place-invariants. Formally, a place-invariant associates weights to the places of the net such that the weighted sum of tokens is not changed by the occurrence of transitions.

We introduce rnodulo-place-invariants of Petri nets which are closely related to classical place-invariants but operate in residue-classes modulo k instead of rational or real numbers. Whereas classical place-invariants prove the non-reachability of a marking if and only if the corresponding marking-equation has no solution in ℚ, a marking can be proved non-reachable by modulo-place-invariants if and only if the marking-equation has no solution in ℤ. Thus, modulo-place-invariants properly generalize classical place-invariants.

Work done within Esprit BR WG 6067: CALIBAN and within SFB 342, WG A3: SEMAFOR.

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Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, 10099, Berlin, Germany

    Jörg Desel

  2. Institut fur Informatik, Technische Universität München, 80290, München, Germany

    Micaela-Daphne Radola

Authors
  1. Jörg Desel
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  2. Micaela-Daphne Radola
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P. S. Thiagarajan

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© 1994 Springer-Verlag Berlin Heidelberg

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Desel, J., Radola, MD. (1994). Proving non-reachability by modulo-place-invariants. In: Thiagarajan, P.S. (eds) Foundation of Software Technology and Theoretical Computer Science. FSTTCS 1994. Lecture Notes in Computer Science, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58715-2_138

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  • DOI: https://doi.org/10.1007/3-540-58715-2_138

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58715-6

  • Online ISBN: 978-3-540-49054-8

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