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Encyclopedia of Mathematics and Its Applications #137: Noncommutative Rational Series with Applications


Encyclopedia of Mathematics and Its Applications #137: Noncommutative Rational Series with Applications Cover


Synopses & Reviews

Publisher Comments:

The algebraic theory of automata was created by Sch tzenberger 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, Sch tzenberger'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.

Book News Annotation:

In the first section, Berstel (emeritus computer science, U. of Paris-Est) and Beutenauer (mathematics, U. of Québec, Montréal) show how formal power series may be viewed as formal languages with coefficients, and how finite automata may be considered as linear representations of the free monoid. Thus, through formal power series, they say, the algebraic theory of automata becomes a part of representation theory. The other sections cover the arithmetic properties of rational series, and applications and important subfamilies of rational series. The text has been used in advanced courses at the many universities where they have taught, and is completely rewritten from their Rational Series and their Languages, for which no date or publisher is cited. Over 170 exercises are provided. Annotation ©2011 Book News, Inc., Portland, OR (

Product Details

Berstel, Jean
Cambridge University Press
Mathematics - Algebra
Publication Date:

Related Subjects

Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Computer
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Physics » Meteorology

Encyclopedia of Mathematics and Its Applications #137: Noncommutative Rational Series with Applications New Hardcover
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Product details pages Cambridge University Press - English 9780521190220 Reviews:
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