Proving Nonreachability by Modulo-Invariants

Abstract We introduce modulo-invariants of Petri nets which are closely related to classical place-invariants but operate in residue classes modulo k instead of natural or rational numbers. Whereas place-invariants prove the nonreachability of a marking if and only if the corresponding marking equation has no solution in Q, a marking can be proved nonreachable by modulo-invariants if and only if the marking equation has no solution in Z. We show how to derive from each net a finite set of invariants — containing place-invariants and modulo-invariants — such that if any invariant proves the nonreachability of a marking, then some invariant of this set proves that the marking is not reachable.

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