Quoridor is PSPACE-Hard
Marius Drop, Benjamin G. Rin, Finn van der Velde

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 . We prove this by reduction from Gpos(POS CNF), a Boolean formula game originally defined in 1978 by T. Schaefer.
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