English

Computational Hardness of Multidimensional Subtraction Games

Computational Complexity 2020-01-14 v1 Computer Science and Game Theory Combinatorics

Abstract

We study algorithmic complexity of solving subtraction games in a~fixed dimension with a finite difference set. We prove that there exists a game in this class such that any algorithm solving the game runs in exponential time. Also we prove an existence of a game in this class such that solving the game is PSPACE-hard. The results are based on the construction introduced by Larsson and W\"astlund. It relates subtraction games and cellular automata.

Keywords

Cite

@article{arxiv.2001.03962,
  title  = {Computational Hardness of Multidimensional Subtraction Games},
  author = {Vladimir Gurvich and Michael Vyalyi},
  journal= {arXiv preprint arXiv:2001.03962},
  year   = {2020}
}
R2 v1 2026-06-23T13:09:03.558Z