Berstel J. Rational Series and Their Languages 2008 torrent

Textbook in PDF format

This book is an introduction to rational formal power series in several noncommutative variables and their relations to formal languages and to the theory of codes.
Formal power series have long been used in all branches of mathematics. They are invaluable in enumeration and combinatorics. For this reason, they are useful in various branches of computer science. As an example, let us mention the study of ambiguity in formal grammars.
It has appeared, for the past twenty years, that rational series in noncommutative variables have many remarkable properties which provide them with a rich structure. Knowledge of these properties makes them much easier to manipulate than, for instance, algebraic series. The depth and number of results for rational series are similar to those for rational languages. The aim of this text is to present the basic results concerning rational series.
This book issued from an advanced course held several times by the authors, at the University Pierre et Marie Curie, Paris and at the University of Saarbrücken. Parts of the book were also taught at several different levels at other places. Any concept from algebra that might not be familiar to the reader can be found in S. Lang’s Algebra (Lang 1984).
This electronic edition of the English edition is at the date of January 8, 2008, a modified version of the original text. New material has been included. It should however remain basically of the same size and of the same algebraic style.
New material: The notion of weighted automaton has been introduced in Chapter I. Systems of equations are considered in the exercises. A new chapter on rational expressions (Chapter IV) is included. Chapter 5 of the first edition has been split into two chapters. The first (Chapter VII) is concerned with Fatou’s property. Positive series in one variable are considered separately in Chapter VIII. A new streamlined proof of Soittola’s theorem is given, incorporating ideas from Perrin’s proof. A new chapter (Chapter XII) on semisimple syntactic algebra has been added.
Many new exercises have been added