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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
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