Automatic Sequences
About this book
Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and formal languages, combinatorics on words.
The text deals with different aspects of automatic sequences, in particular:
· a general introduction to automatic sequences
· the basic (combinatorial) properties of automatic sequences
· the algebraic approach to automatic sequences
· geometric objects related to automatic sequences.
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Information
Table of contents
- Introduction
- 1 Preliminaries
- 1.1 Sequence spaces over groups
- 1.2 The Heisenberg group
- 1.3 Notes and comments
- 2 Expanding endomorphisms and substitutions
- 2.1 Expanding endomorphisms
- 2.2 Substitutions
- 2.3 Notes and comments
- 3 Automaticity
- 3.1 Automatic sequences
- 3.2 Elementary properties of automatic sequences
- 3.3 Notes and comments
- 4 Automaticity II
- 4.1 Automatic subsets
- 4.2 Automatic maps
- 4.3 Automata and automatic maps
- 4.4 Automatic functions on ℕ
- 4.5 Cellular automata and automatic maps
- 4.6 Notes and comments
- 5 Algebraic properties
- 5.1 Additional structure on A̅
- 5.2 Solutions of Mahler equations
- 5.3 Γ abelian
- 5.4 Notes and comments
- Bibliography
- Index
