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Arithmétique et automates finis. (Arithmetic and finite automata). (French) Zbl 0619.10005
Journées arithmétiques, Besançon/France 1985, Astérisque 147/148, 13-26 (1987).
This is a survey about automata problems in arithmetic. Connections with algebraic numbers (or algebraic series over \({\mathbb{F}}_ p(x))\), continued fractions, Dirichlet series, distribution modulo one, harmonic analysis, fractals,... are explained. No proofs are given but a rather complete bibliography is furnished.
For the entire collection see [Zbl 0605.00004].
Reviewer: G.Christol

11A63 Radix representation; digital problems
68Q45 Formal languages and automata
11J81 Transcendence (general theory)