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 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,
Schutzenberger'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.
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