Dots & Boxes is PSPACE-complete
Computational Geometry
2021-05-07 v1 Computational Complexity
Combinatorics
Abstract
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.
Cite
@article{arxiv.2105.02837,
title = {Dots & Boxes is PSPACE-complete},
author = {Kevin Buchin and Mart Hagedoorn and Irina Kostitsyna and Max van Mulken},
journal= {arXiv preprint arXiv:2105.02837},
year = {2021}
}
Comments
18 pages, 13 figures