Reachability in 3-VASS is Elementary
Formal Languages and Automata Theory
2025-04-29 v2 Logic in Computer Science
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.
Keywords
Cite
@article{arxiv.2502.13916,
title = {Reachability in 3-VASS is Elementary},
author = {Wojciech Czerwiński and Ismaël Jecker and Sławomir Lasota and Łukasz Orlikowski},
journal= {arXiv preprint arXiv:2502.13916},
year = {2025}
}