An Fd upper bound for the reachability problem in vector addition systems with states (VASS) in fixed dimension is given, where Fd 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 Fd+4 upper bound due to Leroux and Schmitz (LICS 2019).
@article{arxiv.2404.14781,
title = {Improved Algorithm for Reachability in $d$-VASS},
author = {Yuxi Fu and Qizhe Yang and Yangluo Zheng},
journal= {arXiv preprint arXiv:2404.14781},
year = {2024}
}