Computational Hardness of Multidimensional Subtraction Games

01/12/2020

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by   Vladimir Gurvich, et al.

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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 Wästlund. It relates subtraction games and cellular automata.