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.
Type de document :
[Research Report] RR-1931, INRIA. 1993
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Soumis le : mercredi 24 mai 2006 - 16:13:01
Dernière modification le : mardi 17 avril 2018 - 11:28:43
Document(s) archivé(s) le : mardi 12 avril 2011 - 18:51:04



  • HAL Id : inria-00074743, version 1



Philippe Dumas. Algebraic aspects of B-regular series. [Research Report] RR-1931, INRIA. 1993. 〈inria-00074743〉



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