The algebraic theory of automata was created by Schutzenberger and Chomsky over 50 years ago and there has since been a great deal of development. Classical work on the theory to ncommutative 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 w be more fully explored, in addition to applications in automata theory, codes and n-commutative algebra. Much material, for example, Schutzenberger's theorem on polymially 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.
Jean Berstel is Emeritus Professor of Computer Science in the Gaspard-Monge Institute at Universite Paris-Est, France. Christophe Reutenauer is Professor of Mathematics in the Department of Mathematics at Universite du Quebec ... Montreal.