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On the Complexity of Connection Games

In this paper, we study three connection games among the most widely played: Havannah, Twixt, and Slither. We show that determining the outcome of an arbitrary input position is PSPACE-complete in all three cases. Our reductions are based on the popular graph problem Generalized Geography and on Hex itself. We also consider the complexity of generalizations of Hex parameterized by the length of the solution and establish that while Short Generalized Hex is W[1]-hard, Short Hex is FPT. Finally, we prove that the ultra-weak solution to the empty starting position in hex cannot be fully adapted to any of these three games.

preprint2016arXivOpen access
Édouard BonnetFlorian JamainAbdallah Saffidine
Artificial IntelligenceComputational Complexity
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Open access3 authors2 topics
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Édouard BonnetFlorian JamainAbdallah Saffidine

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