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Computer Science - Theoretical Computer Science | Rational Series and Their Languages

Rational Series and Their Languages

Berstel, Jean, Reutenauer, Christophe

Original French edition by Masson Editeur, Paris 1984

Softcover reprint of the original 1st ed. 1988, VIII, 151 pages.

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  • About this textbook

This book is a systematic exposition of the theory of ratio- nal formal power series and the associated formal languages. It is the first to presentan algebraic approach. It con- tains all fundamental results, starting with the Kleene- Sch}tzenberger theorem, up to the latest developments. Re- lations with number theory and the theory of codes are em- phasized.

Content Level » Research

Related subjects » Number Theory and Discrete Mathematics - Theoretical Computer Science

Table of contents 

I. Rational Series.- 1 Semirings.- 2 Formal Series.- 3 The Topology of K“X”.- 4 Rational Series.- 5 Recognizable Series.- 6 The Fundamental Theorem.- Exercises for Chapter I.- Notes to Chapter I.- II. Minimization.- 1 Syntactic Ideals.- 2 Reduced Linear Representations.- 3 The Reduction Algorithm.- Exercises for Chapter II.- Notes to Chapter II.- III. Series and Languages.- 1 The Theorem of Kleene.- 2 Series and Rational Languages.- 3 Supports.- 4 Iteration.- 5 Complementation.- Exercises for Chapter III.- Notes to Chapter III.- IV. Rational Series in One Variable.- 1 Rational Functions.- 2 The Exponential Polynomial.- 3 A Theorem of Pólya.- 4 A Theorem of Skolem, Mahler and Lech.- Notes to Chapter IV.- V. Changing the Semiring.- 1 Rational Series over a Principal Ring.- 2 Positive Rational Series.- 3 Fatou Extensions.- Exercises for Chapter V.- Notes to Chapter V.- VI. Decidability.- 1 Problems of Supports.- 2 Growth.- Exercises for Chapter VI.- Notes to Chapter VI.- VII. Noncommutative Polynomials.- 1 The Weak Algorithm.- 2 Continuant Polynomials.- 3 Inertia.- 4 Gauss’s Lemma.- Exercises for Chapter VII.- Notes to Chapter VII.- VIII. Codes and Formal Series.- 1 Codes.- 2 Completeness.- 3 The Degree of a Code.- 4 Factorization.- Exercises for Chapter VIII.- Notes to Chapter VIII.- References.

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