In combinatorial game theory, the winning player for a position in normal play is analyzed and characterized via algebraic operations. Such analyses define a value for each position, called a game value. A game (ruleset) is called universal if any game value is achievable in some position in a play of the game. Although the universality of a game implies that the ruleset is rich enough (i.e., sufficiently complex), it does not immediately imply that the game is intractable in the sense of computational complexity. This paper proves that the universal game Turning Tiles is PSPACE-complete.

翻译：在组合博弈论中，正常玩法下某局面的获胜玩家通过代数运算进行分析与刻画。这种分析为每个局面定义了一个被称为博弈值的数值。如果一个游戏（规则集）的任何博弈值都能在该游戏的某个局面中实现，则称该游戏为普适的。尽管游戏的普适性意味着规则集足够丰富（即充分复杂），但这并不直接表明该游戏在计算复杂性意义下是不可解难的。本文证明了普适游戏“翻转瓷砖”是PSPACE完全的。