{"title":"使用中间字母表的密度分类任务顺序解决方案","authors":"Pacôme Perrotin, Pedro Paulo Balbi, Eurico Ruivo","doi":"arxiv-2409.06536","DOIUrl":null,"url":null,"abstract":"We present a sequential cellular automaton of radius 2 1 as a solution to the\ndensity classification task that makes use of an intermediate alphabet, and\nconverges to a clean fixed point with no remaining auxiliary or intermediate\ninformation. We extend this solution to arbitrary finite alphabets and to\nconfigurations in higher dimensions.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"105 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A sequential solution to the density classification task using an intermediate alphabet\",\"authors\":\"Pacôme Perrotin, Pedro Paulo Balbi, Eurico Ruivo\",\"doi\":\"arxiv-2409.06536\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a sequential cellular automaton of radius 2 1 as a solution to the\\ndensity classification task that makes use of an intermediate alphabet, and\\nconverges to a clean fixed point with no remaining auxiliary or intermediate\\ninformation. We extend this solution to arbitrary finite alphabets and to\\nconfigurations in higher dimensions.\",\"PeriodicalId\":501216,\"journal\":{\"name\":\"arXiv - CS - Discrete Mathematics\",\"volume\":\"105 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06536\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06536","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A sequential solution to the density classification task using an intermediate alphabet
We present a sequential cellular automaton of radius 2 1 as a solution to the
density classification task that makes use of an intermediate alphabet, and
converges to a clean fixed point with no remaining auxiliary or intermediate
information. We extend this solution to arbitrary finite alphabets and to
configurations in higher dimensions.
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