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Automata-Theoretic Aspects of Formal Power Series

  • Arto Salomaa
  • Matti Soittola

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

Introduction

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.

Keywords

Automatentheorie Potenzreihe Power Series algebra automata computer formal language formale Sprache

Authors and affiliations

  • Arto Salomaa
    • 1
  • Matti Soittola
    • 1
  1. 1.Department of MathematicsUniversity of TurkuTurku 50Finland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-6264-0
  • Copyright Information Springer-Verlag New York 1978
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6266-4
  • Online ISBN 978-1-4612-6264-0
  • Series Print ISSN 0172-603X
  • Buy this book on publisher's site