The General Vector Addition System Reachability Problem by Presburger Inductive Separators
Résumé
The reachability problem for Vector Addition Systems (VAS) or equivalently for Petri Nets is a central problem of net theory. The general problem is known decidable by algorithms exclusively based on the classical Kosaraju-Lambert-Mayr-Sacerdote-Tenney (KLMST) decomposition. This decomposition is difficult and it just has a non-primitive recursive upper-bound complexity. In this paper, we prove that if a final configuration is not reachable from an initial configuration, there exists a pair of Presburger formulas that denotes an inductive separator proving this property. We deduce an easy algorithm for deciding the reachability problem based on two semi-algorithms. A first one that tries to prove the reachability by fairly enumerating the possible paths and a second one that tries to prove the non-reachability by fairly enumerating pairs of Presburger formulas denoting inductive separators. This algorithm is the very first one that does not require the KLMST decomposition. In particular, this algorithm is the first candidate to obtain a precise (eventually elementary) upper-bound complexity for the VAS reachability problem.
Domaines
AutreOrigine | Fichiers produits par l'(les) auteur(s) |
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