Abstract
An mnk-game is a kind of k-in-a-row game played on an m×n board, where two players alternatively mark empty squares with their own colors and the first player who gets k-consecutive marks (horizontally, vertically, or diagonally) wins. In this paper, we present an AND/OR search tree algorithm specifically for proving mnk-games. We first propose three novel methods to reduce the branching factor of AND/OR search trees. We also propose a new method to find pairing strategies, which further accelerate the proof of mnk-games. The combined methods drastically speed up the proof for the 7,7,5-game, which is solved in 2.5 seconds. Moreover, this paper is the first to solve the 8,8,5-game, which is proven as a draw within 17.4 hours.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
