C. Mauduit: Finite automata and number theory

The seminar is organized by the Formal Model Research Group at the Department of Information Systems, Faculty of Information Technology, Brno University of Technology. As its central scientific topic, it discusses formal models and their applications. Recent presentations are to be found at http://www.fit.vutbr.cz/~meduna/work/doku.php?id=talks:seminar.

Author: Christian MAUDUIT (Institut de Mathématiques de Luminy, Aix-Marseille University, France)
Title: Finite automata and number theory
Abstract: The difficulty of the transition from the representation of an integer in a number system (e.g.  n = 19605131) to its multiplicative representation (e.g. n = 7.13.17.19.23.29) is at the origin of many important open problems in mathematics and in computer science.
        The aim of this talk is to give a survey on recent results concerning the combinatorial, arithmetical and statistical properties of sequences of symbols and sequences of integers generated by finite automata, showing deep connections between number theory, combinatorics, computer science and dynamical systems.
        We will illustrate our talk with some classical examples, including the Thue-Morse sequence, the Rudin-Shapiro sequence and the Cantor sequence.