Algebraic aspects of B-regular series

Philippe Dumas 1
1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : This paper concerns power series of an arithmetic nature that arise in the analysis of divide-and-conquer algorithms. Two key notions are studied : that of B-regular sequence and that of Malherian sequence with their associated power series. Firstly we emphasize the link between rational series over the alphabet {x0, x1,....,xB-1} and B-regular series. Secondly we extend the theorem of Christol, Kamae, Mendes France and Rauzy about automatic sequences and algebraic series to B-regular sequences and Malherian series. We develop here a construtive theory of B-regular and Malherian series. The examples show the ubiquitous character of B-regular series in the study of arithmetic functions related to number representation systems and divide-and-conquer algorithms.
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Philippe Dumas. Algebraic aspects of B-regular series. [Research Report] RR-1931, INRIA. 1993. ⟨inria-00074743⟩

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