Rational Series and Their Languages

Inhaltsverzeichnis

• 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.