Dots Boxes is PSPACE-complete

05/06/2021

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by   Kevin Buchin, et al.

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Exactly 20 years ago at MFCS, Demaine posed the open problem whether the game of Dots Boxes is PSPACE-complete. Dots Boxes has been studied extensively, with for instance a chapter in Berlekamp et al. "Winning Ways for Your Mathematical Plays", a whole book on the game "The Dots and Boxes Game: Sophisticated Child's Play" by Berlekamp, and numerous articles in the "Games of No Chance" series. While known to be NP-hard, the question of its complexity remained open. We resolve this question, proving that the game is PSPACE-complete by a reduction from a game played on propositional formulas.