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2009
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The General Vector Addition System Reachability Problem by Presburger Inductive Invariants

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The General Vector Addition System Reachability Problem by Presburger Inductive Invariants
The reachability problem for Vector Addition Systems (VASs) is a central problem of net theory. The general problem is known decidable by algorithms exclusively based on the classical Kosaraju-Lambert-Mayr-SacerdoteTenney decomposition. This decomposition is used in this paper to prove that the Parikh images of languages accepted by VASs are semi-pseudo-linear; a class that extends the semi-linear sets, a.k.a. the sets definable in the Presburger arithmetic. We provide an application of this result; we prove that a final configuration is not reachable from an initial one if and only if there exists a Presburger formula denoting a forward inductive invariant that contains the initial configuration but not the final one. Since we can decide if a Preburger formula denotes an inductive invariant, we deduce that there exist checkable certificates of non-reachability. In particular, there exists a simple algorithm for deciding the general VAS reachability problem based on two semi-alg...
Jérôme Leroux
Added 24 May 2010
Updated 24 May 2010
Type Conference
Year 2009
Where LICS
Authors Jérôme Leroux
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