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Paper detail

Computational Hardness of Multidimensional Subtraction Games

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.

preprint2020arXivOpen access
Vladimir GurvichMichael Vyalyi
math.COComputer Science and Game TheoryComputational Complexity
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Vladimir GurvichMichael Vyalyi

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