© 1978

Automata-Theoretic Aspects of Formal Power Series


Part of the Texts and Monographs in Computer Science book series (MCS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Arto Salomaa, Matti Soittola
    Pages 1-15
  3. Arto Salomaa, Matti Soittola
    Pages 16-75
  4. Arto Salomaa, Matti Soittola
    Pages 76-117
  5. Arto Salomaa, Matti Soittola
    Pages 118-162
  6. Back Matter
    Pages 163-174

About this book


This book develops a theory of formal power series in noncommuting variables, the main emphasis being on results applicable to automata and formal language theory. This theory was initiated around 196O-apart from some scattered work done earlier in connection with free groups-by M. P. Schutzenberger to whom also belong some of the main results. So far there is no book in existence concerning this theory. This lack has had the unfortunate effect that formal power series have not been known and used by theoretical computer scientists to the extent they in our estimation should have been. As with most mathematical formalisms, the formalism of power series is capable of unifying and generalizing known results. However, it is also capable of establishing specific results which are difficult if not impossible to establish by other means. This is a point we hope to be able to make in this book. That formal power series constitute a powerful tool in automata and language theory depends on the fact that they in a sense lead to the arithmetization of automata and language theory. We invite the reader to prove, for instance, Theorem IV. 5. 3 or Corollaries III. 7. 8 and III. 7.- all specific results in language theory-by some other means. Although this book is mostly self-contained, the reader is assumed to have some background in algebra and analysis, as well as in automata and formal language theory.


Automatentheorie Potenzreihe Power Series algebra automata computer formal language formale Sprache

Authors and affiliations

  1. 1.Department of MathematicsUniversity of TurkuTurku 50Finland

Bibliographic information

  • Book Title Automata-Theoretic Aspects of Formal Power Series
  • Authors Arto Salomaa
    Matti Soittola
  • Series Title Texts and Monographs in Computer Science
  • DOI
  • Copyright Information Springer-Verlag New York 1978
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90282-1
  • Softcover ISBN 978-1-4612-6266-4
  • eBook ISBN 978-1-4612-6264-0
  • Series ISSN 0172-603X
  • Edition Number 1
  • Number of Pages , 171
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Computer Science, general
  • Buy this book on publisher's site
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