English

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

Formal Languages and Automata Theory 2017-03-20 v1 Computational Complexity Logic in Computer Science

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.

Cite

@article{arxiv.1412.4259,
  title  = {Reachability in Two-Dimensional Vector Addition Systems with States is PSPACE-complete},
  author = {Michael Blondin and Alain Finkel and Stefan Göller and Christoph Haase and Pierre McKenzie},
  journal= {arXiv preprint arXiv:1412.4259},
  year   = {2017}
}

Comments

27 pages, 8 figures

R2 v1 2026-06-22T07:30:15.542Z