2021/05/06 by Buchin, Kevin, Hagedoorn, Mart, Kostitsyna, Irina +1 · 1 citation
#Combinatorics (math.CO) #Computational Complexity (cs.CC) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2105.02837
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.