On the Context-Freeness Problem for Vector Addition Systems

Abstract

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.

DOI: 10.1109/LICS.2013.9

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Cite this paper

@article{Leroux2013OnTC, title={On the Context-Freeness Problem for Vector Addition Systems}, author={J{\'e}r{\^o}me Leroux and Vincent Penelle and Gr{\'e}goire Sutre}, journal={2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science}, year={2013}, pages={43-52} }