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Games with Uniqueness Properties

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Abstract

For two-player games of perfect information such as Checkers, Chess, and Go we introduce “uniqueness” properties. A game position has a uniqueness property if a winning strategy—should one exist—is forced to be unique. Depending on the way that winning strategy is forced, a uniqueness property is classified as weak, strong, or global. We prove that any reasonable two-player game G is extendable to a game G * with the strong uniqueness property for both players, so that, e.g., QBF remains PSPACE-complete under this reduction. For global uniqueness, we introduce a simple game over Boolean formulas with this property, and prove that any reasonable two-player game with the global uniqueness property is reducible to it. We show that the class of languages that reduce to globally unique games equals Niedermeier and Rossmanith’s unambiguous alternation class UAP, which is in an interesting region between FewP and SPP.

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Authors and Affiliations

  1. Department of Knowledge-Based Information Engineering, Toyohashi University of Technology, Toyohashi 441-8580, Japan

    Shin Aida

  2. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro-ku Ookayama, Tokyo 152-8552, Japan

    Marcel Crasmaru & Osamu Watanabe

  3. Department of Computer Science, State University of New York at Buffalo, Buffalo, NY 14260-2000, USA

    Kenneth Regan

Authors
  1. Shin Aida
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  2. Marcel Crasmaru
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  3. Kenneth Regan
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  4. Osamu Watanabe
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Corresponding authors

Correspondence to Shin Aida, Marcel Crasmaru, Kenneth Regan or Osamu Watanabe.

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Aida, S., Crasmaru, M., Regan, K. et al. Games with Uniqueness Properties. Theory Comput Systems 37, 29–47 (2004). https://doi.org/10.1007/s00224-003-1105-7

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  • DOI: https://doi.org/10.1007/s00224-003-1105-7

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