{"title":"非经典记数系统中数字的表示","authors":"Christiane Frougny","doi":"10.1109/ARITH.1991.145528","DOIUrl":null,"url":null,"abstract":"Numeration systems, the bases of which are defined by a linear recurrence with integer coefficients, are considered. Conditions on the recurrence are given under which the function of normalization which transforms any representation of an integer into the normal one-obtained by the usual algorithm-can be realized by a finite automaton. Addition is a particular case of normalization. The same questions are discussed for the representation of real numbers in basis theta , where theta is a real number >1. In particular it is shown that, if theta is a Pisot number, then the normalization and the addition in basis theta are computable by a finite automaton.<<ETX>>","PeriodicalId":190650,"journal":{"name":"[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic","volume":"77 2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Representation of numbers in nonclassical numeration systems\",\"authors\":\"Christiane Frougny\",\"doi\":\"10.1109/ARITH.1991.145528\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Numeration systems, the bases of which are defined by a linear recurrence with integer coefficients, are considered. Conditions on the recurrence are given under which the function of normalization which transforms any representation of an integer into the normal one-obtained by the usual algorithm-can be realized by a finite automaton. Addition is a particular case of normalization. The same questions are discussed for the representation of real numbers in basis theta , where theta is a real number >1. In particular it is shown that, if theta is a Pisot number, then the normalization and the addition in basis theta are computable by a finite automaton.<<ETX>>\",\"PeriodicalId\":190650,\"journal\":{\"name\":\"[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic\",\"volume\":\"77 2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.1991.145528\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1991.145528","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Representation of numbers in nonclassical numeration systems
Numeration systems, the bases of which are defined by a linear recurrence with integer coefficients, are considered. Conditions on the recurrence are given under which the function of normalization which transforms any representation of an integer into the normal one-obtained by the usual algorithm-can be realized by a finite automaton. Addition is a particular case of normalization. The same questions are discussed for the representation of real numbers in basis theta , where theta is a real number >1. In particular it is shown that, if theta is a Pisot number, then the normalization and the addition in basis theta are computable by a finite automaton.<>
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