Demystifying Reachability in Vector Addition Systems

Jérôme Leroux 1 Sylvain Schmitz 2, 3
2 DAHU - Verification in databases
LSV - Laboratoire Spécification et Vérification [Cachan], ENS Cachan - École normale supérieure - Cachan, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8643
Abstract : More than 30 years after their inception, the decidability proofs for reachability in vector addition systems (VAS) still retain much of their mystery. These proofs rely crucially on a decomposition of runs successively refined by Mayr, Kosaraju, and Lambert, which appears rather magical, and for which no complexity upper bound is known. We first offer a justification for this decomposition technique, by showing that it computes the ideal decomposition of the set of runs, using the natural embedding relation between runs as well quasi ordering. In a second part, we apply recent results on the complexity of termination thanks to well quasi orders and well orders to obtain a cubic Ackermann upper bound for the decomposition algorithms, thus providing the first known upper bounds for general VAS reachability.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01168388
Contributor : Sylvain Schmitz <>
Submitted on : Thursday, June 25, 2015 - 5:21:05 PM
Last modification on : Tuesday, February 5, 2019 - 1:46:02 PM

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Jérôme Leroux, Sylvain Schmitz. Demystifying Reachability in Vector Addition Systems. LICS 2015, Jul 2015, Kyoto, Japan. pp.56--67, ⟨10.1109/LICS.2015.16⟩. ⟨hal-01168388⟩

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