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Reachability in Symmetric VASS

Authors Łukasz Kamiński , Sławomir Lasota

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ACM Subject Classification
  • Theory of computation → Distributed computing models
Keywords
  • vector addition systems
  • Petri nets
  • reachability problem
  • symmetry
  • permutation group

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Abstract

We investigate the reachability problem in symmetric vector addition systems with states (vass), where transitions are invariant under a group of permutations of coordinates. One extremal case, the trivial groups, yields general vass. In another extremal case, the symmetric groups, we show that the reachability problem can be solved in PSpace, regardless of the dimension of input vass (to be contrasted with Ackermannian complexity in general vass). We also consider other groups, in particular alternating and cyclic ones. Furthermore, motivated by the open status of the reachability problem in data vass, we estimate the gain in complexity when the group arises as a combination of the trivial and symmetric groups.

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Łukasz Kamiński and Sławomir Lasota. Reachability in Symmetric VASS. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 60:1-60:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.60

Author Details

Łukasz Kamiński
  • University of Warsaw, Poland
Sławomir Lasota
  • University of Warsaw, Poland

Funding

  • Kamiński, Łukasz: Partially supported by NCN grant 2021/41/B/ST6/00535.
  • Lasota, Sławomir: Partially supported by the ERC grant INFSYS, agreement no. 950398.

References

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