{"title":"元胞自动机的拓扑共轭分类","authors":"J. Guan, Shaowei Shen","doi":"10.1109/IWCFTA.2009.51","DOIUrl":null,"url":null,"abstract":"We present a theoretically global equivalence classification of cellular automata (CA) on infinite lattices based on the point of view of topological conjugacy. In particular, based on this platform, we further demonstrate that among approximately 1.34×10154 CA rules with nine variables there exists a dual rule of the famous Game of Life, which has been shown to be capable of universal computation, and therefore this rule can also perform universal computation.","PeriodicalId":279256,"journal":{"name":"2009 International Workshop on Chaos-Fractals Theories and Applications","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Topological Conjugacy Classification of Cellular Automata\",\"authors\":\"J. Guan, Shaowei Shen\",\"doi\":\"10.1109/IWCFTA.2009.51\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a theoretically global equivalence classification of cellular automata (CA) on infinite lattices based on the point of view of topological conjugacy. In particular, based on this platform, we further demonstrate that among approximately 1.34×10154 CA rules with nine variables there exists a dual rule of the famous Game of Life, which has been shown to be capable of universal computation, and therefore this rule can also perform universal computation.\",\"PeriodicalId\":279256,\"journal\":{\"name\":\"2009 International Workshop on Chaos-Fractals Theories and Applications\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 International Workshop on Chaos-Fractals Theories and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IWCFTA.2009.51\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Workshop on Chaos-Fractals Theories and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IWCFTA.2009.51","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
基于拓扑共轭的观点，提出了无限格上元胞自动机的理论全局等价分类。特别地，基于这个平台，我们进一步证明了在大约1.34×10154九个变量CA规则中，存在着著名的Game of Life的对偶规则，该对偶规则已被证明能够进行通用计算，因此该规则也可以进行通用计算。
Topological Conjugacy Classification of Cellular Automata
We present a theoretically global equivalence classification of cellular automata (CA) on infinite lattices based on the point of view of topological conjugacy. In particular, based on this platform, we further demonstrate that among approximately 1.34×10154 CA rules with nine variables there exists a dual rule of the famous Game of Life, which has been shown to be capable of universal computation, and therefore this rule can also perform universal computation.
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