Proving non-reachability by modulo-place-invariants

  • Jörg Desel
  • Micaela-Daphne Radola
Part of the Lecture Notes in Computer Science book series (LNCS, volume 880)


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 , 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.


Petri nets Reachability analysis Invariants 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jörg Desel
    • 1
  • Micaela-Daphne Radola
    • 2
  1. 1.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institut fur InformatikTechnische Universität MünchenMünchenGermany

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