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Noncommutative Rational Series with Applications


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: October 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521190220

£ 106.00

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About the Authors
  • 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.

    • A comprehensive exposition of the theory
    • Includes numerous number-theoretic applications and a new proof of Soittola's theorem
    • An excellent resource for graduate students and researchers
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    Product details

    • Date Published: October 2010
    • format: Hardback
    • isbn: 9780521190220
    • length: 262 pages
    • dimensions: 240 x 160 x 19 mm
    • weight: 0.54kg
    • contains: 3 b/w illus. 170 exercises
    • availability: Available
  • Table of Contents

    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
    Index of notation

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    Noncommutative Rational Series with Applications

    Jean Berstel, Christophe Reutenauer

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  • Authors

    Jean Berstel, Université Paris-Est
    Jean Berstel is Emeritus Professor of Computer Science in the Gaspard-Monge Institute at Université Paris-Est, France.

    Christophe Reutenauer, Université du Québec à Montréal
    Christophe Reutenauer is Professor of Mathematics in the Department of Mathematics at Université du Québec à Montréal.

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