An $\mathsf{F}_{d}$ upper bound for the reachability problem in vector addition systems with states (VASS) in fixed dimension is given, where $\mathsf{F}_d$ is the $d$-th level of the Grzegorczyk hierarchy of complexity classes. The new algorithm combines the idea of the linear path scheme characterization of the reachability in the $2$-dimension VASSes with the general decomposition algorithm by Mayr, Kosaraju and Lambert. The result improves the $\mathsf{F}_{d + 4}$ upper bound due to Leroux and Schmitz (LICS 2019).

翻译：针对固定维度的带状态向量添加系统（VASS）中的可达性问题，给出了一个 $\mathsf{F}_{d}$ 上界，其中 $\mathsf{F}_d$ 是 Grzegorczyk 复杂度层级中的第 $d$ 级。该新算法将 2-维 VASS 中可达性的线性路径方案刻画思想与 Mayr、Kosaraju 和 Lambert 的通用分解算法相结合。这一结果改进了 Leroux 和 Schmitz（LICS 2019）提出的 $\mathsf{F}_{d + 4}$ 上界。