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

Lecomte, P.; Rigo, M.

Theory Comput. Syst. 35, No. 1, 13-38 (2002).

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