Theory of linear and integer programming
Theory of linear and integer programming
Decidability of a temporal logic problem for petri nets
IDTC Second international conference on Database theory
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)
How to Compose Presburger-Accelerations: Applications to Broadcast Protocols
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
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
Journal of Computer and System Sciences
Vector addition system reachability problem: a short self-contained proof
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Flat counter automata almost everywhere!
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
Presburger Vector Addition Systems
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
Presburger Vector Addition Systems
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
| Hi-index | 0.00 |
The reach ability problem for Vector Addition Systems (VAS) is a central problem of net theory. The problem is known to be decidable by inductive invariants definable in the Presburger arithmetic. When the reach ability set is definable in the Presburger arithmetic, the existence of such an inductive invariant is immediate. However, in this case, the computation of a Presburger formula denoting the reach ability set is an open problem. In this paper we close this problem by proving that if the reach ability set of a VAS is definable in the Presburger arithmetic, then the VAS is flatable, i.e. its reach ability set can be obtained by runs labeled by words in a bounded language. As a direct consequence, classical algorithms based on acceleration techniques effectively compute a formula in the Presburger arithmetic denoting the reach ability set.