The context-freeness of the languages associated with vector addition systems is decidable
Theoretical Computer Science
A note on fine covers and iterable factors of VAS languages
Information Processing Letters
The Complexity of the Finite Containment Problem for Petri Nets
Journal of the ACM (JACM)
Petri nets and regular processes
Journal of Computer and System Sciences
Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
The Mathematical Theory of Context-Free Languages
The Mathematical Theory of Context-Free Languages
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
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
A Perfect Model for Bounded Verification
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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Petri nets, or equivalently vector addition systems (VAS), are widely recognized as a central model for concurrent systems. Many interesting properties are decidable for this class, such as bounded ness, reach ability, regularity, as well as context-freeness, which is the focus of this paper. The context-freeness problem asks whether the trace language of a given VAS is context-free. This problem was shown to be decidable by Schwer in 1992, but the proof is very complex and intricate. The resulting decision procedure relies on five technical conditions over a customized cover ability graph. These five conditions are shown to be necessary, but the proof that they are sufficient is only sketched. In this paper, we revisit the context-freeness problem for VAS, and give a simpler proof of decidability. Our approach is based on witnesses of non-context-freeness, that are bounded regular languages satisfying a nesting condition. As a corollary, we obtain that the trace language of a VAS is context-free if, and only if, it has a context-free intersection with every bounded regular language.