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arXiv · 2602.05315

On the Reachability Problem for One-Dimensional Thin Grammar Vector Addition Systems

Chengfeng Xue·Yuxi Fu
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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.

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Chengfeng Xue, Yuxi Fu. 2026-02-05. On the Reachability Problem for One-Dimensional Thin Grammar Vector Addition Systems. https://arxiv.org/abs/2602.05315

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