Ebook: Automatic sequences

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.