Theory of linear and integer programming
Theory of linear and integer programming
A structure to decide reachability in Petri nets
Theoretical Computer Science
The Complexity of the Finite Containment Problem for Petri Nets
Journal of the ACM (JACM)
Decidability of reachability in vector addition systems (Preliminary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
An algorithm for the general Petri net reachability problem
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
The decidability of the reachability problem for vector addition systems (Preliminary Version)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
The General Vector Addition System Reachability Problem by Presburger Inductive Invariants
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Livelock and deadlock detection for PA inter-organizational business processes
EGOVIS'12/EDEM'12 Proceedings of the 2012 Joint international conference on Electronic Government and the Information Systems Perspective and Electronic Democracy, and Proceedings of the 2012 Joint international conference on Advancing Democracy, Government and Governance
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A central problem of net theory is the reachability problem for Vector Addition Systems (VASs). The general problem is known to be decidable by algorithms exclusively based on the classical Kosaraju-Lambert-Mayr-Sacerdote-Tenney 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 non-reachability in the Presburger arithmetic. In particular, there exists a simple algorithm for deciding the general VAS reachability problem based on two semi-algorithms. A first one that tries to prove the reachability by enumerating finite sequences of actions and a second one that tries to prove the non-reachability by enumerating Presburger formulas. In this paper we provide 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, inspired from Hauschildt, that directly proves the existence of Presburger inductive invariants.