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DOI: 10.4230/LIPIcs.MFCS.2025.22

On the Reachability Problem for Two-Dimensional Branching VASS

Authors: Clotilde Bizière, Thibault Hilaire, Jérôme Leroux, and Grégoire Sutre

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

Vectors addition systems with states (VASS), or equivalently Petri nets, are arguably one of the most studied formalisms for the modeling and analysis of concurrent systems. A central decision problem for VASS is reachability: whether there exists a run from an initial configuration to a final one. This problem has been known to be decidable for over forty years, and its complexity has recently been precisely characterized. Our work concerns the reachability problem for BVASS, a branching generalization of VASS. In dimension one, the exact complexity of this problem is known. In this paper, we prove that the reachability problem for 2-dimensional BVASS is decidable. In fact, we even show that the reachability set admits a computable semilinear presentation. The decidability status of the reachability problem for BVASS remains open in higher dimensions.

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Clotilde Bizière, Thibault Hilaire, Jérôme Leroux, and Grégoire Sutre. On the Reachability Problem for Two-Dimensional Branching VASS. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{biziere_et_al:LIPIcs.MFCS.2025.22,
  author =	{Bizi\`{e}re, Clotilde and Hilaire, Thibault and Leroux, J\'{e}r\^{o}me and Sutre, Gr\'{e}goire},
  title =	{{On the Reachability Problem for Two-Dimensional Branching VASS}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.22},
  URN =		{urn:nbn:de:0030-drops-241294},
  doi =		{10.4230/LIPIcs.MFCS.2025.22},
  annote =	{Keywords: Vector addition systems, Reachability problem, Semilinear sets, Verification}
}

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On the Reachability Problem for Two-Dimensional Branching VASS

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