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

Diego Figueira (1, 2) , Ranko Lazić (3) , Jérôme Leroux (1, 2) , Filip Mazowiecki (3) , Grégoire Sutre (1, 2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 CNRS - Centre National de la Recherche Scientifique
3 University of Warwick [Coventry]

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.

Domaines: Base de données [cs.DB]; Théorie et langage formel [cs.FL]; Mathématique discrète [cs.DM]; Logique en informatique [cs.LO]

Diego Figueira, Ranko Lazić, Jérôme Leroux, Filip Mazowiecki, Grégoire Sutre. Polynomial-Space Completeness of Reachability for Succinct Branching VASS in Dimension One. International Colloquium on Automata, Languages, and Programming (ICALP), Jul 2017, Varsovie, Poland. pp.119, ⟨10.4230/LIPIcs.ICALP.2017.119⟩. ⟨hal-01688742⟩