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Computational complexity of Turning Tiles

Author

Listed:
  • Tesshu Hanaka

    (Kyushu University)

  • Hironori Kiya

    (Osaka Metropolitan University)

  • Hirotaka Ono

    (Nagoya University)

  • Koki Suetsugu

    (National Institute of Informatics
    Waseda University)

  • Kanae Yoshiwatari

    (Nagoya University)

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.

Suggested Citation

  • Tesshu Hanaka & Hironori Kiya & Hirotaka Ono & Koki Suetsugu & Kanae Yoshiwatari, 2024. "Computational complexity of Turning Tiles," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(4), pages 1211-1222, December.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:4:d:10.1007_s00182-024-00908-0
    DOI: 10.1007/s00182-024-00908-0
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