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Exploring VASS Parameterised by Geometric Dimension

Authors Wojciech Czerwiński , Roland Guttenberg , Łukasz Orlikowski , Henry Sinclair-Banks , Yangluo Zheng

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LIPIcs.ICALP.2026.177.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Parallel computing models
Keywords
  • vector addition systems
  • Petri nets
  • geometric dimensions
  • coverability problem
  • integer reachability problem
  • simultaneous unboundedness
  • reachability problem

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Abstract

The geometric dimension g of a Vector Addition System with States (VASS) is the dimension of the vector space generated by cycles in the VASS; this parameter refines the standard dimension d, the number of counters. Recently, it was discovered that the fastest-known algorithm for solving the reachability problem for VASS has the same complexity in terms of g as in terms of d. This suggests that the geometric dimension may in fact be a more adequate parameter for measuring the complexity of VASS reachability problems. We initiate a more systematic study of the geometric dimension. We discuss differences between two parameters: the geometric dimension and the SCC dimension. Our main technical result states that classical results about the coverability and boundedness problems can be improved from dimension d to geometric dimension g. Namely, coverability is witnessed by runs of length n^{2^𝒪(g)} instead of n^{2^𝒪(d)}, and unboundedness can be witnessed by runs of length n^{2^𝒪(g log g)} instead of n^{2^𝒪(d log d)}, where n is the size of the instance. We also study integer reachability and simultaneous unboundedness in VASS parameterised by the geometric dimension.

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Wojciech Czerwiński, Roland Guttenberg, Łukasz Orlikowski, Henry Sinclair-Banks, and Yangluo Zheng. Exploring VASS Parameterised by Geometric Dimension. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 177:1-177:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.177

Author Details

Wojciech Czerwiński
  • University of Warsaw, Poland
Roland Guttenberg
  • University of Warsaw, Poland
Łukasz Orlikowski
  • University of Warsaw, Poland
Henry Sinclair-Banks
  • University of Warsaw, Poland
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany
Yangluo Zheng
  • BASICS, Shanghai Jiao Tong University, China

Funding

The first four authors are supported by the ERC grant INFSYS, agreement no. 950398. Yangluo Zheng is supported by the NSFC (Natural Science Foundation of China) grant no. 62572319.

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