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arXiv · 1412.4259

Reachability in Two-Dimensional Vector Addition Systems with States is PSPACE-complete

Michael Blondin·Alain Finkel·Stefan Göller·Christoph Haase·Pierre McKenzie
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Abstract

Determining the complexity of the reachability problem for vector addition systems with states (VASS) is a long-standing open problem in computer science. Long known to be decidable, the problem to this day lacks any complexity upper bound whatsoever. In this paper, reachability for two-dimensional VASS is shown PSPACE-complete. This improves on a previously known doubly exponential time bound established by Howell, Rosier, Huynh and Yen in 1986. The coverability and boundedness problems are also noted to be PSPACE-complete. In addition, some complexity results are given for the reachability problem in two-dimensional VASS and in integer VASS when numbers are encoded in unary.

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Michael Blondin, Alain Finkel, Stefan Göller, Christoph Haase, Pierre McKenzie. 2014-12-13. Reachability in Two-Dimensional Vector Addition Systems with States is PSPACE-complete. https://doi.org/10.1109/lics.2015.14

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