Computational Hardness of Multidimensional Subtraction Games

Vladimir Gurvich; Michael Vyalyi

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arXiv · 2001.03962

Computational Hardness of Multidimensional Subtraction Games

Vladimir Gurvich·Michael Vyalyi

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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.

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Vladimir Gurvich, Michael Vyalyi. 2020-01-12. Computational Hardness of Multidimensional Subtraction Games. https://arxiv.org/abs/2001.03962

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