A Polynomial-Time Algorithm for Reachability in Branching VASS in Dimension One

Authors Stefan Göller, Christoph Haase, Ranko Lazic, Patrick Totzke

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Stefan Göller
Christoph Haase
Ranko Lazic
Patrick Totzke

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Stefan Göller, Christoph Haase, Ranko Lazic, and Patrick Totzke. A Polynomial-Time Algorithm for Reachability in Branching VASS in Dimension One. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 105:1-105:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


Branching VASS (BVASS) generalise vector addition systems with states by allowing for special branching transitions that can non-deterministically distribute a counter value between two control states. A run of a BVASS consequently becomes a tree, and reachability is to decide whether a given configuration is the root of a reachability tree. This paper shows P-completeness of reachability in BVASS in dimension one, the first decidability result for reachability in a subclass of BVASS known so far. Moreover, we show that coverability and boundedness in BVASS in dimension one are P-complete as well.
  • branching vector addition systems
  • reachability
  • coverability
  • boundedness


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