Quoridor is PSPACE-Hard

TL;DR

This paper proves that determining a winning strategy in Quoridor, an abstract strategy game, is PSPACE-complete, by reducing from a known Boolean formula game, highlighting its computational complexity.

Contribution

It establishes the PSPACE-completeness of Quoridor, a popular abstract game, through a reduction from Gpos(POS CNF), a classic Boolean formula game.

Findings

Determines the computational complexity of Quoridor as PSPACE-complete.

Provides a reduction from Gpos(POS CNF) to Quoridor.

Highlights the difficulty of solving general Quoridor positions.

Abstract

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.