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## Proving Nonreachability by Modulo-Invariants.

Desel, J.;
Neuendorf, K.-P.;
Radola, M.-D.
In:
*Theoretical Computer Science Vol. 153, No. 1--2*, pages 49-64.
1996.

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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