亚马逊游戏的增强型求解器

Q2 Computer Science

IEEE Transactions on Computational Intelligence and AI in Games Pub Date : 2015-03-01 DOI:10.1109/TCIAIG.2014.2309077

Jiaxing Song, Martin Müller

{"title":"亚马逊游戏的增强型求解器","authors":"Jiaxing Song, Martin Müller","doi":"10.1109/TCIAIG.2014.2309077","DOIUrl":null,"url":null,"abstract":"The game of Amazons is a modern board game with simple rules and nice mathematical properties. It has a high computational complexity. In 2001, the starting position on a 5 × 5 board was proven to be a first player win. The enhanced Amazons solver presented here extends previous work in the following five ways: by building more powerful endgame databases, including a new type of databases for so-called blocker territories, by improving the rules for computing bounds on complex game positions, by local search to find tighter local bounds, by using ideas from combinatorial game theory to find wins earlier, and by using a df-pn based solver. Using the improved solver, the starting positions for Amazons on the 4 × 5, 5 × 4, 4 × 6, 5 × 6, and 4 × 7 boards were shown to be first player wins, while 6 × 4 is a second player win. The largest proof, for the 5 × 6 board, is presented in detail.","PeriodicalId":49192,"journal":{"name":"IEEE Transactions on Computational Intelligence and AI in Games","volume":"7 1","pages":"16-27"},"PeriodicalIF":0.0000,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1109/TCIAIG.2014.2309077","citationCount":"7","resultStr":"{\"title\":\"An Enhanced Solver for the Game of Amazons\",\"authors\":\"Jiaxing Song, Martin Müller\",\"doi\":\"10.1109/TCIAIG.2014.2309077\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The game of Amazons is a modern board game with simple rules and nice mathematical properties. It has a high computational complexity. In 2001, the starting position on a 5 × 5 board was proven to be a first player win. The enhanced Amazons solver presented here extends previous work in the following five ways: by building more powerful endgame databases, including a new type of databases for so-called blocker territories, by improving the rules for computing bounds on complex game positions, by local search to find tighter local bounds, by using ideas from combinatorial game theory to find wins earlier, and by using a df-pn based solver. Using the improved solver, the starting positions for Amazons on the 4 × 5, 5 × 4, 4 × 6, 5 × 6, and 4 × 7 boards were shown to be first player wins, while 6 × 4 is a second player win. The largest proof, for the 5 × 6 board, is presented in detail.\",\"PeriodicalId\":49192,\"journal\":{\"name\":\"IEEE Transactions on Computational Intelligence and AI in Games\",\"volume\":\"7 1\",\"pages\":\"16-27\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1109/TCIAIG.2014.2309077\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Transactions on Computational Intelligence and AI in Games\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/TCIAIG.2014.2309077\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Computer Science\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Computational Intelligence and AI in Games","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TCIAIG.2014.2309077","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Computer Science","Score":null,"Total":0}

引用次数: 7

摘要

亚马逊的游戏是一个现代棋盘游戏与简单的规则和良好的数学性质。它具有很高的计算复杂度。2001年，在5 × 5棋盘上的起始位置被证明是第一个玩家获胜。本文提出的增强型amazon解算器在以下五个方面扩展了以前的工作:通过构建更强大的终局数据库，包括所谓的阻塞区域的新型数据库，通过改进复杂博弈位置计算边界的规则，通过局部搜索找到更紧密的局部边界，通过使用组合博弈论的思想找到更早的胜利，以及通过使用基于df-pn的解算器。使用改进的解算器，亚马逊在4 × 5、5 × 4、4 × 6、5 × 6和4 × 7棋盘上的起始位置显示为第一个玩家获胜，而6 × 4是第二个玩家获胜。最大的证明，为5 × 6板，详细介绍。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An Enhanced Solver for the Game of Amazons

The game of Amazons is a modern board game with simple rules and nice mathematical properties. It has a high computational complexity. In 2001, the starting position on a 5 × 5 board was proven to be a first player win. The enhanced Amazons solver presented here extends previous work in the following five ways: by building more powerful endgame databases, including a new type of databases for so-called blocker territories, by improving the rules for computing bounds on complex game positions, by local search to find tighter local bounds, by using ideas from combinatorial game theory to find wins earlier, and by using a df-pn based solver. Using the improved solver, the starting positions for Amazons on the 4 × 5, 5 × 4, 4 × 6, 5 × 6, and 4 × 7 boards were shown to be first player wins, while 6 × 4 is a second player win. The largest proof, for the 5 × 6 board, is presented in detail.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

IEEE Transactions on Computational Intelligence and AI in Games COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Cessation. The IEEE Transactions on Computational Intelligence and AI in Games (T-CIAIG) publishes archival journal quality original papers in computational intelligence and related areas in artificial intelligence applied to games, including but not limited to videogames, mathematical games, human–computer interactions in games, and games involving physical objects. Emphasis is placed on the use of these methods to improve performance in and understanding of the dynamics of games, as well as gaining insight into the properties of the methods as applied to games. It also includes using games as a platform for building intelligent embedded agents for the real world. Papers connecting games to all areas of computational intelligence and traditional AI are considered.