Automatic Synthesis of Generalized Winning Strategies of Impartial Combinatorial Games Using SMT Solvers
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
Main track. Pages 1703-1711. https://doi.org/10.24963/ijcai.2020/236
Strategy representation and reasoning has recently received much attention in artificial intelligence. Impartial combinatorial games (ICGs) are a type of elementary and fundamental games in game theory. One of the challenging problems of ICGs is to construct winning strategies, particularly, generalized winning strategies for possibly infinitely many instances of ICGs. In this paper, we investigate synthesizing generalized winning strategies for ICGs. To this end, we first propose a logical framework to formalize ICGs based on the linear integer arithmetic fragment of numeric part of PDDL. We then propose an approach to generating the winning formula that exactly captures the states in which the player can force to win. Furthermore, we compute winning strategies for ICGs based on the winning formula. Experimental results on several games demonstrate the effectiveness of our approach.
Knowledge Representation and Reasoning: Action, Change and Causality
Knowledge Representation and Reasoning: Knowledge Representation and Game Theory; Social Choice
Agent-based and Multi-agent Systems: Formal Verification, Validation and Synthesis
Planning and Scheduling: Distributed;Multi-agent Planning