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On the Representation of Real Numbers Using Regular Languages

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Abstract.

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.

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Authors and Affiliations

  1. Institut de Mathématiques, Université de Liège, {plecomte,M.Rigo}@ulg.ac.be, Grande Traverse 12 (B 37), B-4000 Liège, Belgium, BE

    P. Lecomte & M. Rigo

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  1. P. Lecomte
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  2. M. Rigo
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Received February 13, 2001, and in final form September 21, 2001. Online publication January 14, 2002.

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Lecomte, P., Rigo, M. On the Representation of Real Numbers Using Regular Languages. Theory Comput. Systems 35, 13–38 (2002). https://doi.org/10.1007/s00224-001-1007-5

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  • DOI: https://doi.org/10.1007/s00224-001-1007-5

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