Polynomial-Space Completeness of Reachability for Succinct Branching VASS in Dimension One

Authors Diego Figueira, Ranko Lazic, Jérôme Leroux, Filip Mazowiecki, Grégoire Sutre

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Diego Figueira
Ranko Lazic
Jérôme Leroux
Filip Mazowiecki
Grégoire Sutre

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Diego Figueira, Ranko Lazic, Jérôme Leroux, Filip Mazowiecki, and Grégoire Sutre. Polynomial-Space Completeness of Reachability for Succinct Branching VASS in Dimension One. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 119:1-119:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Whether the reachability problem for branching vector addition systems, or equivalently the provability problem for multiplicative exponential linear logic, is decidable has been a long-standing open question. The one-dimensional case is a generalisation of the extensively studied one-counter nets, and it was recently established polynomial-time complete provided counter updates are given in unary. Our main contribution is to determine the complexity when the encoding is binary: polynomial-space complete.
  • branching vector addition systems
  • reachability problem


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