{"title":"皇帝的新递归性:指数函数在两个可计算模型中的注解","authors":"V. Brattka","doi":"10.1142/9789812704979_0005","DOIUrl":null,"url":null,"abstract":"In his book \\The Emperor’s New Mind\" Roger Penrose implicitly denes some criteria which should be met by a reasonable notion of recursiveness for subsets of Euclidean space. We discuss two such notions with regard to Penrose’s criteria: one originated from computable analysis, and the one introduced by Blum, Shub and Smale.","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"39","resultStr":"{\"title\":\"The Emperor's New Recursiveness: The Epigraph of the Exponential Function in Two Models of Computability\",\"authors\":\"V. Brattka\",\"doi\":\"10.1142/9789812704979_0005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In his book \\\\The Emperor’s New Mind\\\" Roger Penrose implicitly denes some criteria which should be met by a reasonable notion of recursiveness for subsets of Euclidean space. We discuss two such notions with regard to Penrose’s criteria: one originated from computable analysis, and the one introduced by Blum, Shub and Smale.\",\"PeriodicalId\":265391,\"journal\":{\"name\":\"Words, Languages & Combinatorics\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2003-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"39\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Words, Languages & Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789812704979_0005\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Words, Languages & Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789812704979_0005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Emperor's New Recursiveness: The Epigraph of the Exponential Function in Two Models of Computability
In his book \The Emperor’s New Mind" Roger Penrose implicitly denes some criteria which should be met by a reasonable notion of recursiveness for subsets of Euclidean space. We discuss two such notions with regard to Penrose’s criteria: one originated from computable analysis, and the one introduced by Blum, Shub and Smale.
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