Download PDFOpen PDF in browserVector Addition Systems Reachability Problem (A Simpler Solution)15 pages•Published: June 22, 2012AbstractThe reachability problem for Vector Addition Systems (VASs) is a central problem of net theory. The general problem is known to be decidable by algorithms based on the classical KosarajuLambertMayrSacerdoteTenney decomposition (KLMTS decomposition). Recently from this decomposition, we deduced that a final configuration is not reachable from an initial one if and only if there exists a Presburger 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 from this result that there exist checkable certificates of nonreachability in the Presburger arithmetic. In particular, there exists a simple algorithm for deciding the general VAS reachability problem based on two semialgorithms. A first one that tries to prove the reachability by enumerating finite sequences of actions and a second one that tries to prove the nonreachability by enumerating Presburger formulas. In another recent paper we provided the first proof of the VAS reachability problem that is not based on the KLMST decomposition. The proof is based on the notion of production relations that directly proves the existence of Presburger inductive invariants. In this paper we propose new intermediate results simplifying a bit more this last proof.Keyphrases: Petri net, Presburger arithmetic, reachability problem, VAS In: Andrei Voronkov (editor). Turing100. The Alan Turing Centenary, vol 10, pages 214228
