Turning Tiles is PSPACE-complete

TL;DR

This paper proves that the game Turning Tiles, which can produce any game value, is computationally intractable, specifically PSPACE-complete, highlighting its complexity despite universality.

Contribution

It establishes that Turning Tiles is PSPACE-complete, linking universality with computational complexity in combinatorial game theory.

Findings

Turning Tiles is universal, capable of achieving any game value.

Turning Tiles is proven to be PSPACE-complete.

The complexity of Turning Tiles is intractable despite its universality.

Abstract

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.