Quoridor is an award-winning abstract strategy game designed by Mirko Marchesi and published in 1997. Similar games include Maze Attack, Blockade (also known as Cul-de-sac), and Pinko Pallino. In line with chess, checkers, Go, and other classic combinatorial games, Quoridor is a turn-based, deterministic, perfect-information game played on a square grid. We show that it is PSPACE-complete to determine whether a given player has a winning strategy in a given Quoridor position on a board with size $n \times n$. We prove this by reduction from Gpos(POS CNF), a Boolean formula game originally defined in 1978 by T. Schaefer.

翻译：Quoridor是一款获奖的抽象策略游戏，由Mirko Marchesi设计并于1997年发布。相似游戏包括Maze Attack、Blockade（亦称Cul-de-sac）和Pinko Pallino。与国际象棋、跳棋、围棋及其他经典组合游戏一样，Quoridor是一种回合制、确定性、完全信息游戏，在正方形网格上进行。我们证明，在规模为$n \times n$的棋盘上判定给定玩家在特定Quoridor局面中是否存在获胜策略是PSPACE完全的。这一结论通过从Gpos(POS CNF)（一种由T. Schaefer于1978年最初定义的布尔公式游戏）进行归约而得证。