Lower Bounds for the Reachability Problem in Fixed Dimensional VASSes

TL;DR

This paper establishes new lower bounds on the computational complexity of the reachability problem in fixed-dimensional Vector Addition Systems with States (VASSes), demonstrating increasing hardness with higher dimensions and different encoding schemes.

Contribution

The paper provides four improved lower bounds for the reachability problem in fixed-dimensional VASSes, advancing the understanding of their computational complexity.

Findings

NP-hardness for unary flat 4-VASSes

PSPACE-hardness for unary 5-VASSes

EXPSPACE-hardness for binary 6-VASSes

Abstract

We study the complexity of the reachability problem for Vector Addition Systems with States (VASSes) in fixed dimensions. We provide four lower bounds improving the currently known state-of-the-art: 1) \np-hardness for unary flat $4$-VASSes (VASSes in dimension 4), 2) \pspace-hardness for unary $5$-VASSes, 3) \expspace-hardness for binary $6$-VASSes and 4) \tower-hardness for unary $8$-VASSes.