An Easy Algorithm For The General Vector Addition System Reachability Problem

Jérôme Leroux (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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 configuration is not reachable from an initial configuration, there exists a semi-linear inductive invariant that proves 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 semi-linear inductive invariants. This algorithm is the very first one that does not require the KLMST decomposition. In particular, this algorithm should be a good candidate to obtain a precise (eventually elementary) upper-bound complexity for the VAS reachability problem.

Mots clés: Semi-linear; Presburger Arithmetic; Vector Addition Systems; Reachability

Domaines: Autre

Jérôme Leroux. An Easy Algorithm For The General Vector Addition System Reachability Problem. 2008. ⟨hal-00272667v4⟩