On the Complexity of Connection Games
Computational Complexity
2016-05-17 v1 Artificial Intelligence
Abstract
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.
Cite
@article{arxiv.1605.04715,
title = {On the Complexity of Connection Games},
author = {Édouard Bonnet and Florian Jamain and Abdallah Saffidine},
journal= {arXiv preprint arXiv:1605.04715},
year = {2016}
}
Comments
Subsumes and extends https://arxiv.org/abs/1403.6518 significantly