Minimal solutions of linear diophantine systems: bounds and algorithms
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
The context-freeness of the languages associated with vector addition systems is decidable
Theoretical Computer Science
A unified approach for deciding the existence of certain Petri net paths
Information and Computation
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
Journal of Computer and System Sciences
Model checking coverability graphs of vector addition systems
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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We introduce a logic for specifying trace properties of vector addition systems (VAS). This logic can express linear relations among pumping segments occurring in a trace. Given a VAS and a formula in the logic, we investigate the question whether the VAS contains a trace satisfying the formula. Our main contribution is an exponential space upper bound for this problem. The proof is based on a small model property for the logic. Compared to similar logics that are solvable in exponential space, a distinguishing feature of our logic is its ability to express non-context-freeness of the trace language of a VAS. This allows us to show that the context-freeness problem for VAS, whose complexity was not established so far, is ExpSpace-complete.