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Reachability in Vector Addition System with States Parameterized by Geometric Dimension

Author Yangluo Zheng

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

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Abstract

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).

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Yangluo Zheng. Reachability in Vector Addition System with States Parameterized by Geometric Dimension. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CONCUR.2025.38

Author Details

Yangluo Zheng
  • BASICS, Shanghai Jiao Tong University, China

Funding

The support from the National Science Foundation of China (62072299), Science and Technology Commission of Shanghai Municipality (24BC3200500) are acknowledged.

Acknowledgements

The author would like to thank Wojciech Czerwiński, Łukasz Orlikowski and Qizhe Yang for a fruitful discussion which motivates Section 5. The author also thanks the members of BASICS for their interest. The efforts of anonymous reviewers are appreciated.

References

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