Year: 2026
Type: preprint
Abstract: Vector addition systems with states (VASS) are a classic model in concurrency theory. Grammar vector addition systems (GVAS), equivalently, pushdown VASS, extend VASS by using a context-free grammar to control addition. In this paper, our main focus is on the reachability problem for one-dimensional thin GVAS (thin 1-GVAS), a structurally restricted yet expressive subclass. By adopting the index measure for complexity, and by generalizing the decomposition technique developed in the study of VASS reachability to grammar-generated derivation trees of GVAS, an effective integer programming system is established for a thin 1-GVAS. In this way, a nondeterministic algorithm with $\mathbf{F}_{2k}$ complexity is obtained for the reachability of thin 1-GVAS with index $k$, yielding a tighter upper bound than the previous one.
Source: arXiv (Cornell University)
Authors: Xue, Chengfeng, Fu, Yuxi
Institution: Shanghai Jiao Tong University
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7128015131
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