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Havannah and TwixT are PSPACE-complete

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Computers and Games (CG 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8427))

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Abstract

Numerous popular abstract strategy games ranging from Hex and Havannah via TwixT and Slither to Lines of Action belong to the class of connection games. Still, very few complexity results on such games have been obtained since Hex was proved pspace-complete in the early 1980s.

We study the complexity of two connection games among the most widely played ones, i.e., we prove that Havannah and TwixT are pspace-complete. The proof for Havannah involves a reduction from Generalized Geography and is based solely on ring-threats to represent the input graph. The reduction for TwixT builds up on previous work as it is a straightforward encoding of Hex.

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Notes

  1. 1.

    For a summary in English of Reisch’s reduction, see Maarup’s thesis [17].

  2. 2.

    See www.boardability.com/game.php?id=twixt and www.grappa.univ-lille3.fr/icga/ game.php?id=37 for details.

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Authors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Paris, France

    Édouard Bonnet, Florian Jamain & Abdallah Saffidine

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  1. Édouard Bonnet
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  2. Florian Jamain
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  3. Abdallah Saffidine
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Correspondence to Abdallah Saffidine .

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Editors and Affiliations

  1. Tilburg University, Tilburg, The Netherlands

    H. Jaap van den Herik

  2. JAIST, Ishikawa, Japan

    Hiroyuki Iida

  3. Tilburg University, Tilburg, The Netherlands

    Aske Plaat

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Bonnet, É., Jamain, F., Saffidine, A. (2014). Havannah and TwixT are PSPACE-complete. In: van den Herik, H., Iida, H., Plaat, A. (eds) Computers and Games. CG 2013. Lecture Notes in Computer Science(), vol 8427. Springer, Cham. https://doi.org/10.1007/978-3-319-09165-5_15

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  • DOI: https://doi.org/10.1007/978-3-319-09165-5_15

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  • Print ISBN: 978-3-319-09164-8

  • Online ISBN: 978-3-319-09165-5

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