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Quantified Boolean Solving for Achievement Games

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KI 2021: Advances in Artificial Intelligence (KI 2021)

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Abstract

Recent developments in the propositional representation of achievement games have renewed interest in applying the latest advances in Quantified Boolean Formula technologies to solving these games. However, the number of quantifier alternations necessary to explore the solution space still impairs and limits the applicability of these methods. In this paper, we show that one can encode blocking strategies for the second player and express the last moves of the play with a single string of existential quantifiers, instead of the usual alternations of universal and existential quantifiers. We experimentally show that our method improves the performance of state-of-the-art Quantified Boolean Formula solvers on Harary’s Tic-Tac-Toe, a well-known achievement game.

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Authors and Affiliations

  1. Department of Computer Science, UQAM, Montreal, Canada

    Steve Boucher & Roger Villemaire

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  1. Steve Boucher
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  2. Roger Villemaire
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Correspondence to Roger Villemaire .

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Editors and Affiliations

  1. Czech Technical University in Prague, Prague, Czech Republic

    Stefan Edelkamp

  2. University of Lübeck, Lübeck, Germany

    Ralf Möller

  3. University of Leoben, Leoben, Austria

    Elmar Rueckert

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Boucher, S., Villemaire, R. (2021). Quantified Boolean Solving for Achievement Games. In: Edelkamp, S., Möller, R., Rueckert, E. (eds) KI 2021: Advances in Artificial Intelligence. KI 2021. Lecture Notes in Computer Science(), vol 12873. Springer, Cham. https://doi.org/10.1007/978-3-030-87626-5_3

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  • DOI: https://doi.org/10.1007/978-3-030-87626-5_3

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  • Print ISBN: 978-3-030-87625-8

  • Online ISBN: 978-3-030-87626-5

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