Computational complexity of Turning Tiles

Tesshu Hanaka (), Hironori Kiya (), Hirotaka Ono (), Koki Suetsugu () and Kanae Yoshiwatari ()
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Tesshu Hanaka: Kyushu University
Hironori Kiya: Osaka Metropolitan University
Hirotaka Ono: Nagoya University
Koki Suetsugu: National Institute of Informatics
Kanae Yoshiwatari: Nagoya University

International Journal of Game Theory, 2024, vol. 53, issue 4, No 7, 1222 pages

Abstract: 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. We also give other positive and negative results on the computational complexity of Turning Tiles.

Keywords: Combinatorial game theory; Computational complexity; Winning strategy; Turning tiles; DP-hardness (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00182-024-00908-0

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