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Computational Hardness of Multidimensional Subtraction Games (2001.03962v1)
Published 12 Jan 2020 in cs.CC, cs.GT, and math.CO
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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