Improved Algorithm for Reachability in d-VASS

An mathsfFd upper bound for the reachability problem in vector addition systems with states (VASS) in fixed dimension is given, where mathsfFd 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 mathsfFd + 4 upper bound due to Leroux and Schmitz (LICS 2019).