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arXiv · 2506.22561

On the Reachability Problem for Two-Dimensional Branching VASS

Clotilde Bizière·Thibault Hilaire·Jérôme Leroux·Grégoire Sutre
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Abstract

Vectors addition systems with states (VASS), or equivalently Petri nets, are arguably one of the most studied formalisms for the modeling and analysis of concurrent systems. A central decision problem for VASS is reachability: whether there exists a run from an initial configuration to a final one. This problem has been known to be decidable for over forty years, and its complexity has recently been precisely characterized. Our work concerns the reachability problem for BVASS, a branching generalization of VASS. In dimension one, the exact complexity of this problem is known. In this paper, we prove that the reachability problem for 2-dimensional BVASS is decidable. In fact, we even show that the reachability set admits a computable semilinear presentation. The decidability status of the reachability problem for BVASS remains open in higher dimensions.

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Clotilde Bizière, Thibault Hilaire, Jérôme Leroux, Grégoire Sutre. 2025-06-27. On the Reachability Problem for Two-Dimensional Branching VASS. https://arxiv.org/abs/2506.22561

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