Noncommutative Rational Series with Applications
Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Preface; Part I: Rational series; 1 Rational series; 1.1 Semirings; 1.2 Formal series; 1.3 Topology; 1.4 Rational series; 1.5 Recognizable series; 1.6 Weighted automata; 1.7 The fundamental theorem; Exercises for Chapter 1; Notes to Chapter 1; 2 Minimization; 2.1 Syntactic ideals; 2.2 Minimal linear representations; 2.3 The minimization algorithm; Exercises for Chapter 2; Notes to Chapter 2; 3 Series and languages; 3.1 Klee…
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- Full title :Noncommutative Rational Series with Applications.
Summary
Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Preface; Part I: Rational series; 1 Rational series; 1.1 Semirings; 1.2 Formal series; 1.3 Topology; 1.4 Rational series; 1.5 Recognizable series; 1.6 Weighted automata; 1.7 The fundamental theorem; Exercises for Chapter 1; Notes to Chapter 1; 2 Minimization; 2.1 Syntactic ideals; 2.2 Minimal linear representations; 2.3 The minimization algorithm; Exercises for Chapter 2; Notes to Chapter 2; 3 Series and languages; 3.1 Kleene's theorem; 3.2 Series and rational languages; 3.3 Syntactic algebras and syntactic monoids.
3.4 Support3.5 Iteration; 3.6 Complementation; Exercises for Chapter 3; Notes to Chapter 3; 4 Rational expressions; 4.1 Rational expressions; 4.2 Rational identities over a ring; 4.3 Star height; 4.4 Absolute star height; Exercises for Chapter 4; Notes to Chapter 4; Part II: Arithmetic; 5 Automatic sequences and algebraic series; 5.1 Regular functions; 5.2 Stable submodules and operations on k-regular functions; 5.3 Automatic sequences; 5.4 Automatic sequences and algebraic series; 5.5 Algebraic series and diagonals of rational series; Exercises for Chapter 5; Notes to Chapter 5.
6 Rational series in one variable6.1 Rational functions; 6.2 The exponential polynomial; 6.3 A theorem of Pólya; 6.4 A theorem of Skolem, Mahler, Lech; Exercises for Chapter 6; Notes to Chapter 6; 7 Changing the semiring; 7.1 Rational series over a principal ring; 7.2 Fatou extensions; 7.3 Polynomial identities and rationality criteria; 7.4 Fatou ring extensions; Exercises for Chapter 7; Notes to Chapter 7; 8 Positive series in one variable; 8.1 Poles of positive rational series; 8.2 Polynomially bounded series over Z and N; 8.3 Characterization of K+ -rational series; 8.4 Star height 2.
Exercises for Chapter 8Notes to Chapter 8; Part III: Applications; 9 Matrix semigroups and applications; 9.1 Finite matrix semigroups and the Burnside problem; 9.2 Polynomial growth; 9.3 Limited languages and the tropical semiring; Exercises for Chapter 9; Notes to Chapter 9; 10 Noncommutative polynomials; 10.1 The weak algorithm; 10.2 Continuant polynomials; 10.3 Inertia; 10.4 Gauss's Lemma; Exercises for Chapter 10; Notes to Chapter 10; 11 Codes and formal series; 11.1 Codes; 11.2 Completeness; 11.3 The degree of a code; 11.4 Factorization; Exercises for Chapter 11; Notes to Chapter 11.
12 Semisimple syntactic algebras12.1 Bifix codes; 12.2 Cyclic languages; Appendix 1: Semisimple algebras; Appendix 2: Minimal ideals in finite monoids; Exercises for Chapter 12; Notes to Chapter 12; Open problems and conjectures; References; Index of notation; Index.
A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science.
Edition Statements
- Publication Date:2010.
- Edition:Online-ausg
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:2010.
The Physical Object
- Description:Online-Ressource (1 online resource (264 Seiten))
Edition Identifiers
- ISBN:9781107269774, 1107269776, 9780521190220, 0521190223, 9780511760860, 0511760868
- DOI:10.1017/CBO9780511760860
- oclc:ocn852654321
- LC Classification:QA267 .B47 2011
- Dewey Decimal:511.35
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