{"title":"任意环上计算的Blum-Shub-Smale理论中程序的表示","authors":"Hu Xiao-Long","doi":"10.1145/166589.166596","DOIUrl":null,"url":null,"abstract":"In the paper \"On a Theory of Computation and Complexity over the Real Numbers: NP Completeness, Recursive Functions and Universal machines\" (BSS 1989), the authors, Lenore Blum, Mike Shub, and Steve Smale, generalize the notion of computability from the set of natural numbers to an arbitrary ordered ring. In particular they discuss the existence of a Universal Machine over such a ring and the \"godel\" number or \"code\" of machines defined on such a ring. In this short paper we wish to correct some minor error in their definition of a \"code\" of a machine.","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The representation of a program in the Blum-Shub-Smale theory of computation over an arbitrary ring\",\"authors\":\"Hu Xiao-Long\",\"doi\":\"10.1145/166589.166596\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the paper \\\"On a Theory of Computation and Complexity over the Real Numbers: NP Completeness, Recursive Functions and Universal machines\\\" (BSS 1989), the authors, Lenore Blum, Mike Shub, and Steve Smale, generalize the notion of computability from the set of natural numbers to an arbitrary ordered ring. In particular they discuss the existence of a Universal Machine over such a ring and the \\\"godel\\\" number or \\\"code\\\" of machines defined on such a ring. In this short paper we wish to correct some minor error in their definition of a \\\"code\\\" of a machine.\",\"PeriodicalId\":388781,\"journal\":{\"name\":\"Bull. EATCS\",\"volume\":\"45 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bull. EATCS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/166589.166596\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bull. EATCS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/166589.166596","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The representation of a program in the Blum-Shub-Smale theory of computation over an arbitrary ring
In the paper "On a Theory of Computation and Complexity over the Real Numbers: NP Completeness, Recursive Functions and Universal machines" (BSS 1989), the authors, Lenore Blum, Mike Shub, and Steve Smale, generalize the notion of computability from the set of natural numbers to an arbitrary ordered ring. In particular they discuss the existence of a Universal Machine over such a ring and the "godel" number or "code" of machines defined on such a ring. In this short paper we wish to correct some minor error in their definition of a "code" of a machine.
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