Abstract
Let β be a real number β 1. Addition and multiplication by a fixed positive integer of real numbers represented in base β are shown to be computable by an on-line algorithm, and thus are continuous functions. When β is a Pisot number, these functions are computable by an on-line finite automaton.
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Frougny, C. (1999). On-Line Addition in Real Base. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_1
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DOI: https://doi.org/10.1007/3-540-48340-3_1
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