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Méthodes algorithmiques pour la résolution des jeux combinatoires

Julien Lemoine 1 
1 SMAC - Systèmes Multi-Agents et Comportements
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : The aim of this thesis is to determine algorithms that help to solve combinatorial games by computation. First, we explain how the implementation of the nimber speeds up the computation of impartial games in normal version. Then, we propose refinements or generalizations of tree-traversal algorithms, especially the PN-search, while discussing the benefit of human intervention during the execution of these algorithms. Finally, we present verification algorithms, whose initial goal was to ensure the validity of our computation, but also allowed us to obtain small solution trees. We have applied these methods to the game of Sprouts, where players connect dots with lines, and Dots-and-boxes, where players complete boxes by drawing edges. Sprouts is an impartial combinatorial game, whose topological nature makes it difficult to represent for a computer. We explain such a representation, before studying a generalization where the game is played on compact surfaces. Dots-and-boxes is a partizan game, and we detail various theoretical simplifications that allowed us to compute new results for this game.
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https://tel.archives-ouvertes.fr/tel-00839385
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Submitted on : Monday, July 1, 2013 - 1:38:02 AM
Last modification on : Tuesday, November 22, 2022 - 2:26:15 PM
Long-term archiving on: : Wednesday, October 2, 2013 - 4:10:35 AM

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  • HAL Id : tel-00839385, version 1

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Julien Lemoine. Méthodes algorithmiques pour la résolution des jeux combinatoires. Intelligence artificielle [cs.AI]. Université des Sciences et Technologie de Lille - Lille I, 2011. Français. ⟨NNT : ⟩. ⟨tel-00839385⟩

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