Reachability in Vector Addition System with States Parameterized by Geometric Dimension
Zheng, Yangluo · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2025
The geometric dimension of a vector addition system with states (VASS), emerged in Leroux and Schmitz (2019) and formalized by Fu, Yang, and Zheng (2024), quantifies the dimension of the vector space spanned by cycle effects in the system. This paper examines the VASS reachability problem through the lens of geometric dimension, revealing key differences from the traditional dimensional parameterization. Notably, we establish that the reachability problem for both geometrically 1-dimensional and 2-dimensional VASS is PSPACE-complete, achieved by extending the pumping technique initially proposed by Czerwiński et al. (2019).