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
Model checking coverability graphs of vector addition systems
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
The reachability problem for vector addition system with one zero-test
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Vector addition system reversible reachability problem
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Decidability of LTL for vector addition systems with one zero-test
RP'11 Proceedings of the 5th international conference on Reachability problems
Using real relaxations during program specialization
LOPSTR'11 Proceedings of the 21st international conference on Logic-Based Program Synthesis and Transformation
Bounded context-switching and reentrant locking
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
On selective unboundedness of VASS
Journal of Computer and System Sciences
Analysis of Recursively Parallel Programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Well-Structured pushdown systems
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Presburger Vector Addition Systems
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
Reasoning about Data Repetitions with Counter Systems
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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The reachability problem for Vector Addition Systems (VASs) 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 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 provides the existence of Presburger inductive invariants.