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arXiv · 2607.09558

Solving the Reachability Problem for Branching Vector Addition Systems via Semilinear Inductive Invariants

Clotilde Bizière·Jérôme Leroux·Grégoire Sutre
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Abstract

In this paper, we solve the reachability problem for branching vector addition systems (BVAS), a long standing open problem. Our approach is based on semilinear inductive invariants. More precisely, we prove that if a configuration of a BVAS is not reachable, then there exists an inductive invariant, given as a semilinear set, that does not contain this configuration. Based on this property, we deduce a very simple (enumerative) algorithm solving the reachability problem for BVAS.

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Clotilde Bizière, Jérôme Leroux, Grégoire Sutre. 2026-07-10. Solving the Reachability Problem for Branching Vector Addition Systems via Semilinear Inductive Invariants. https://arxiv.org/abs/2607.09558

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