2024/12/19 by Yangluo Zheng, Zheng, Yangluo
Computer Science · #Matrix Theory and Algorithms #Optimization and Search Problems #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.2412.14608
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 explores 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 originally proposed by Czerwiński et al. (2019).