Automatic Sequences Theory, Applications, Generalizations [Hardcover]

This book is the first integrated treatment of sequences generated by finite automata and their generalizations.This book, combining concepts of mathematics and computer science, is about the sequences of symbols that can be generated by simple models of computation called finite automata . Suitable for graduate students or advanced undergraduates, the book starts from first principles and develops the basic theory. Then it shows how these ideas can be applied to solve problems in number theory and physics.This book, combining concepts of mathematics and computer science, is about the sequences of symbols that can be generated by simple models of computation called finite automata . Suitable for graduate students or advanced undergraduates, the book starts from first principles and develops the basic theory. Then it shows how these ideas can be applied to solve problems in number theory and physics.Combining concepts of mathematics and computer science, this book is about the sequences of symbols that can be generated by simple models of computation called finite automata . Suitable for graduate students or advanced undergraduates, it starts from elementary principles and develops the basic theory. The study then progresses to show how these ideas can be applied to solve problems in number theory and physics.Preface; 1. Stringology; 2. Number theory and algebra; 3. Numeration systems; 4. Finite automata and other models of computation; 5. Automatic sequences; 6. Uniform morphisms and automatic sequences; 7. Morphic sequences; 8. Frequency of letters; 9. Characteristic words; 10. Subwords; 11. Cobham's theorem; 12. Formal power series; 13. Automatic real numbers; 14. Multidimensional automatic sequences; 15. Automaticity; 16. k-regular sequences; 17. Physics; Appendix. Hints, references and solutions for selected exercises; Bibliography; Index. [A] fine book...I highly recommend Automatic Sequences, whether as text, reference, or all the more as an excellent l3"