On the Context-Freeness Problem for Vector Addition Systems

Jérôme Leroux (1) , Vincent Penelle (2) , Grégoire Sutre (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

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 boundedness, reachability, 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 coverability 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.

Domaines: Logique en informatique [cs.LO]

Jérôme Leroux, Vincent Penelle, Grégoire Sutre. On the Context-Freeness Problem for Vector Addition Systems. LICS 2013, Jun 2013, New Orleans, LA, United States. pp.43-52, ⟨10.1109/LICS.2013.9⟩. ⟨hal-00788744v2⟩