Berstel J., Reutenauer C. Noncommutative Rational Series with Applications

Cambridge University Press, 2010, -249 p.This book is issued from a previous book of the authors, entitled Rational Series and their Languages. The present text is an entirely rewritten, and enriched version of this book. An important part of the material presented here appears for the first time in book form.
The text served for advanced courses held several times by the authors, at the University Pierre et Marie Curie, Paris and at the University of Saarbrucken. Parts of the book were also taught at several different levels at other places, such as the University of Quebec at Montreal and the University of Marne-la-Vallee.Part I Rational series
Rational series
Minimization
Series and languages
Rational expressions
Part II Arithmetic
Automatic sequences and algebraic series
Rational series in one variable
Changing the semiring
Positive series in one variable
Part III Applications
Matrix semigroups and applications
Noncommutative polynomials
Codes and formal series
Semisimple syntactic algebras