Titlebook: Sequences, Groups, and Number Theory; Valérie Berthé,Michel Rigo Book 2018 Springer International Publishing AG, part of Springer Nature 2

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Normal Numbers and Computer Science,nteger base if its expansion in that base is such that all blocks of digits of the same length occur in it with the same limiting frequency. This chapter is an introduction to the theory of normal numbers. We present five different equivalent formulations of normality, and we prove their equivalence

Chronological

Normal Numbers and Symbolic Dynamics,ch as periodicity, uniqueness, randomness, etc. from the orbit. Starting with a description of the link between dynamical systems and numeration systems, we present the concept of normal and non-normal numbers providing different views on the dynamics of the system. Normal numbers are “normal” with

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institute

Automaton (Semi)groups: Wang Tilings and Schreier Tries,ontributing to important conjectures in group theory. In the current chapter, we intend to provide various combinatorial and dynamical tools to tackle some decision problems all related to some extent to the growth of automaton (semi)groups. In the first part, we consider Wang tilings as a major too

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Infelicity

Number Theoretic Aspects of Regular Sequences, then examine size and growth properties of regular sequences. The last half of the chapter focuses on the algebraic, analytic, and Diophantine properties of Mahler functions. In particular, we survey the rational-transcendental dichotomies of Mahler functions, due to Bézivin, and of regular numbers, due to Bell, Bugeaud, and Coons.

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