{"type":"ScholarlyArticle","title":"Automatic Synthesis of Generalized Winning Strategies of Impartial Combinatorial Games Using SMT Solvers","authors":[{"name":"Kaisheng Wu","slug":"kaisheng-wu","given":"Kaisheng","family":"Wu","affiliation":"Department of Computer Science , Jinan University , China"},{"name":"Liangda Fang","slug":"liangda-fang","given":"Liangda","family":"Fang","affiliation":"Department of Computer Science , Jinan University , China; Guangxi Key Laboratory of Trusted Software , Guilin University of Electronic Technology , China"},{"name":"Liping Xiong","slug":"liping-xiong","given":"Liping","family":"Xiong","affiliation":"Department of Computer Science , South China Normal University , China"},{"name":"Zhao-Rong Lai","slug":"zhao-rong-lai","given":"Zhao-Rong","family":"Lai","affiliation":"Department of Computer Science , Jinan University , China"},{"name":"Yong Qiao","slug":"yong-qiao","given":"Yong","family":"Qiao","affiliation":"Department of Computer Science , Jinan University , China"},{"name":"Kaidong Chen","slug":"kaidong-chen","given":"Kaidong","family":"Chen","affiliation":"Department of Computer Science , Jinan University , China"},{"name":"Fei Rong","slug":"fei-rong","given":"Fei","family":"Rong","affiliation":"Department of Computer Science , Jinan University , China"}],"abstract":"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.","doi":"10.24963/ijcai.2020/236","url":"https://ijcai.org/proceedings/2020/236","pdf":"https://ijcai.org/proceedings/2020/0236.pdf","markdown":"https://ijcai.org/proceedings/2020/236.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/236","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":236,"pages":{"first":1703,"last":1711},"keywords":["Knowledge Representation and Reasoning: Knowledge Representation and  Game Theory; Social Choice","Planning and Scheduling: Distributed;Multi-agent Planning","Agent-based and Multi-agent Systems: Formal Verification, Validation and Synthesis","Knowledge Representation and Reasoning: Action, Change and Causality"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25515/file_25515.m3u8","length_sec":221,"provider":"hls"}],"references":[{"position":1,"raw":"[Ahn et al., 2017] June Ahn, Benjamin Chen, Richard Chen, Ezra Erives, Jeremy Fleming, Michael Gerovitch, Tejas Gopalakr- ishna, Tanya Khovanova, Neil Malur, Nastia Polina, and Poonam Sahoo. 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