On the representation of real numbers using regular languages

被引：11

作者：

Lecomte, P ^{[1
]}

Rigo, M ^{[1
]}

机构：

[1] Univ Liege, Inst Math, B-4000 Liege, Belgium

来源：

THEORY OF COMPUTING SYSTEMS | 2002年 / 35卷 / 01期

关键词：

Real Number; Numerical Approximation; Algebraic Number; Convergent Sequence; Regular Language;

D O I：

10.1007/s00224-001-1007-5

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Using a lexicographically ordered regular language, we show how to represent an interval of R. We determine exactly the possible representations of any element in this interval and study the function which maps a representation onto its numerical value. We make explicit the relationship between the convergence of finite words to an infinite word and the convergence of the corresponding approximations to a real number.

引用

页码：13 / 38

页数：26

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