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arXiv · 2502.13916

Reachability in 3-VASS is Elementary

Wojciech Czerwiński·Ismaël Jecker·Sławomir Lasota·Łukasz Orlikowski
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Abstract

The reachability problem in 3-dimensional vector addition systems with states (3-VASS) is known to be PSpace-hard, and to belong to Tower. We significantly narrow down the complexity gap by proving the problem to be solvable in doubly-exponential space. The result follows from a new upper bound on the length of the shortest path: if there is a path between two configurations of a 3-VASS then there is also one of at most triply-exponential length. We show it by introducing a novel technique of approximating the reachability sets of 2-VASS by small semi-linear sets.

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Wojciech Czerwiński, Ismaël Jecker, Sławomir Lasota, Łukasz Orlikowski. 2025-02-19. Reachability in 3-VASS is Elementary. https://arxiv.org/abs/2502.13916

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