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.
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}
}