{"title":"可分性和状态复杂性","authors":"Klaus Sutner","doi":"10.3888/TMJ.11.3-8","DOIUrl":null,"url":null,"abstract":"It is well known that the set of all natural numbers divisible by a fixed modulus m can be recognized by a finite state machine, assuming that the numbers are written in standard base-B representation. It is much harder to determine the state complexity of the minimal recognizer [1]. In this article we discuss the size of minimal recognizers for a variety of numeration systems, including reverse base-B representation and the Fibonacci system.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"11 1","pages":"430-445"},"PeriodicalIF":0.0000,"publicationDate":"2010-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Divisibility and State Complexity\",\"authors\":\"Klaus Sutner\",\"doi\":\"10.3888/TMJ.11.3-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is well known that the set of all natural numbers divisible by a fixed modulus m can be recognized by a finite state machine, assuming that the numbers are written in standard base-B representation. It is much harder to determine the state complexity of the minimal recognizer [1]. In this article we discuss the size of minimal recognizers for a variety of numeration systems, including reverse base-B representation and the Fibonacci system.\",\"PeriodicalId\":91418,\"journal\":{\"name\":\"The Mathematica journal\",\"volume\":\"11 1\",\"pages\":\"430-445\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-02-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Mathematica journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3888/TMJ.11.3-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Mathematica journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3888/TMJ.11.3-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is well known that the set of all natural numbers divisible by a fixed modulus m can be recognized by a finite state machine, assuming that the numbers are written in standard base-B representation. It is much harder to determine the state complexity of the minimal recognizer [1]. In this article we discuss the size of minimal recognizers for a variety of numeration systems, including reverse base-B representation and the Fibonacci system.
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