Description

A comprehensive reference on the theory of variable-length codes and their relation to automata. A major revision of Berstel and Perrin's classic Theory of Codes, this book has been written with a more modern focus and a much broader coverage of the subject. It is a comprehensive reference on the theory of variable-length codes and their relation to automata. A major revision of Berstel and Perrin's classic Theory of Codes, this book has been written with a more modern focus and a much broader coverage of the subject. It is a comprehensive reference on the theory of variable-length codes and their relation to automata. This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In sum this is a comprehensive reference on the theory of variable-length codes and their relation to automata. Preface; 1. Preliminaries; 2. Codes; 3. Prefix codes; 4. Automata; 5. Deciphering delay; 6. Bifix codes; 7. Circular codes; 8. Factorizations of free monoids; 9. Unambiguous monoids of relations; 10. Synchronization; 11. Groups of codes; 12. Factorizations of cyclic groups; 13. Densities; 14. Polynomials of finite codes; Solutions of exercises; Appendix: Research problems; References; Index of notation; Index. "For undergraduates, this synergy of many basic subjects should make an ideal capstone course. In addition, abstract algebra students always need practical applications and computer science students always need to see the "pure" mathematics; the material in this work can serve both ends."
D.V. Feldman, Choice Magazine