Abstract
We study the 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 solving the game is EXP-complete and requires time 2Ω(n), where n is the input size. This bound is optimal up to a polynomial speed-up. The results are based on a construction introduced by Larsson and Wästlund. It relates subtraction games and cellular automata.
Funder
Russian Science Foundation
Subject
Computational Mathematics,Computational Theory and Mathematics,Numerical Analysis,Theoretical Computer Science
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