Description

A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science. Starting where Schützenberger and Chomsky left off, the authors present to an audience of graduate students and researchers a modern account of the subject and its applications. This is an excellent resource and reference for all those working in algebra, theoretical computer science and their areas of overlap. Starting where Schützenberger and Chomsky left off, the authors present to an audience of graduate students and researchers a modern account of the subject and its applications. This is an excellent resource and reference for all those working in algebra, theoretical computer science and their areas of overlap. The algebraic theory of automata was created by Schützenberger and Chomsky over 50 years ago and there has since been a great deal of development. Classical work on the theory to noncommutative power series has been augmented more recently to areas such as representation theory, combinatorial mathematics and theoretical computer science. This book presents to an audience of graduate students and researchers a modern account of the subject and its applications. The algebraic approach allows the theory to be developed in a general form of wide applicability. For example, number-theoretic results can now be more fully explored, in addition to applications in automata theory, codes and non-commutative algebra. Much material, for example, Schützenberger's theorem on polynomially bounded rational series, appears here for the first time in book form. This is an excellent resource and reference for all those working in algebra, theoretical computer science and their areas of overlap. Preface; Part I. Rational Series: 1. Rational series; 2. Minimization; 3. Series and languages; 4. Rational expressions; Part II. Arithmetic: 5. Automatic sequences and algebraic series; 6. Rational series in one variable; 7. Changing the semiring; 8. Positive series in one variable; Part III. Applications: 9. Matrix semigroups and applications; 10. Noncommutative polynomials; 11. Codes and formal series; 12. Semisimple syntactic algebras; Open problems and conjectures; References; Index of notation; Index. "This well-written volume is much more than a mere reprint. This comprehensive reference on rational series has been rewritten and new material has been added."
Michel Rigo, Mathematical Reviews