Abstract
We prove that the function of normalization in base θ, which maps any θ-representation of a real number onto its θ-development, obtained by a greedy algorithm, is a function computable by a finite automaton over any alphabet if and only if θ is a Pisot number.
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Christiane Frougny was supported in part by the PRC Mathématiques et Informatique of the Ministère de la Recherche et de l'Espace.
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Berend, D., Frougny, C. Computability by finite automata and pisot bases. Math. Systems Theory 27, 275–282 (1994). https://doi.org/10.1007/BF01578846
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DOI: https://doi.org/10.1007/BF01578846