The reachability problem for vector addition systems with states (VASS) has been shown to be \textsc{Ackermann}-complete. For every $k\geq 3$, a completeness result for the $k$-dimensional VASS reachability problem is not yet available. It is shown in this paper that the $3$-dimensional VASS reachability problem is in \textsc{Tower}, improving upon the current best upper bound $\mathbf{F}_7$ established by Leroux and Schmidt in 2019.

翻译：带状态向量加法系统（VASS）的可达性问题已被证明是Ackermann完全的。对于每个$k\geq 3$，$k$维VASS可达性问题的完全性结果尚不可得。本文证明三维VASS可达性问题属于Tower复杂度类，改进了Leroux和Schmidt于2019年建立的最佳上界$\mathbf{F}_7$。