On-line digit set conversion in real base

Authors:
Christiane Frougny
Affiliations:
Université Paris 8, Départment d'Informatique, 2 Rue de la Liberté, 93526 Saint-Denis Cedex, France and L.I.A.F.A., UMR 7089, Case 7014, 2 place Jussieu, F-75251 Paris Cedex 05, Fra ...
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

Let β be a real number 1. The digit set conversion between real numbers represented in fixed base β is shown to be computable by an on-line algorithm, and thus is a continuous function. When β is a Pisot number the digit set conversion is computable by an on-line finite automaton.