## On the representation of real numbers using regular languages.(English)Zbl 0993.68050

Summary: Using a lexicographically ordered regular language, we show how to represent an interval of $$\mathbb R$$. 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.

### MSC:

 68Q45 Formal languages and automata 68R15 Combinatorics on words 11A67 Other number representations

### Keywords:

lexicographically ordered regular language
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