{"title":"冯诺依曼规则、分裂性和初等元胞自动机","authors":"Ville Salo","doi":"10.4230/OASIcs.AUTOMATA.2021.11","DOIUrl":null,"url":null,"abstract":"We show that a cellular automaton on a mixing subshift of finite type is a Von Neumann regular element in the semigroup of cellular automata if and only if it is split epic onto its image in the category of sofic shifts and block maps. It follows from [S.-T\\\"orm\\\"a, 2015] that Von Neumann regularity is decidable condition, and we decide it for all elementary CA.","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Von Neumann regularity, split epicness and elementary cellular automata\",\"authors\":\"Ville Salo\",\"doi\":\"10.4230/OASIcs.AUTOMATA.2021.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that a cellular automaton on a mixing subshift of finite type is a Von Neumann regular element in the semigroup of cellular automata if and only if it is split epic onto its image in the category of sofic shifts and block maps. It follows from [S.-T\\\\\\\"orm\\\\\\\"a, 2015] that Von Neumann regularity is decidable condition, and we decide it for all elementary CA.\",\"PeriodicalId\":124625,\"journal\":{\"name\":\"International Workshop on Cellular Automata and Discrete Complex Systems\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Workshop on Cellular Automata and Discrete Complex Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Workshop on Cellular Automata and Discrete Complex Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Von Neumann regularity, split epicness and elementary cellular automata
We show that a cellular automaton on a mixing subshift of finite type is a Von Neumann regular element in the semigroup of cellular automata if and only if it is split epic onto its image in the category of sofic shifts and block maps. It follows from [S.-T\"orm\"a, 2015] that Von Neumann regularity is decidable condition, and we decide it for all elementary CA.
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