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arXiv · 2608.04786

Reachability in 3-VAS

Łukasz Kamiński·Sławomir Lasota
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Abstract

We settle the exact complexity of the reachability problem in (stateless) vector addition systems (VAS) in fixed low dimension. In dimensions 2-4 it has only been known to be sandwiched between NP and PSPACE. We prove PSPACE-hardness of the reachability problem for symmetric vector addition systems in dimension 3 (3-VAS), a restricted fragment of general 3-VAS. Combined with previously established PSPACE upper bounds, our result settles the complexity of the problem to be PSPACE-complete in 3-VAS and 4-VAS, as well as in their symmetric fragments.

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Łukasz Kamiński, Sławomir Lasota. 2026-08-05. Reachability in 3-VAS. https://arxiv.org/abs/2608.04786

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