Improved Algorithm for Reachability in d-VASS

Authors Yuxi Fu, Qizhe Yang , Yangluo Zheng



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Author Details

Yuxi Fu
  • BASICS, Shanghai Jiao Tong University, China
Qizhe Yang
  • Shanghai Normal University, China
Yangluo Zheng
  • BASICS, Shanghai Jiao Tong University, China

Acknowledgements

We thank Weijun Chen, Huan Long, Hao Wu and Qiang Yin for proofreading various versions of this paper.

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Yuxi Fu, Qizhe Yang, and Yangluo Zheng. Improved Algorithm for Reachability in d-VASS. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 136:1-136:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.136

Abstract

An 𝖥_{d} upper bound for the reachability problem in vector addition systems with states (VASS) in fixed dimension is given, where 𝖥_d is the d-th level of the Grzegorczyk hierarchy of complexity classes. The new algorithm combines the idea of the linear path scheme characterization of the reachability in the 2-dimension VASSes with the general decomposition algorithm by Mayr, Kosaraju and Lambert. The result improves the 𝖥_{d + 4} upper bound due to Leroux and Schmitz (LICS 2019).

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Logic and verification
Keywords
  • Petri net
  • vector addition system
  • reachability

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