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Iteration Theories

The Equational Logic of Iterative Processes

  • Stephen L. Bloom
  • Zoltán Ésik

Part of the EATCS Monographs on Theoretical Computer Science book series (EATCS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Stephen L. Bloom, Zoltán Ésik
    Pages 1-6
  3. Stephen L. Bloom, Zoltán Ésik
    Pages 7-21
  4. Stephen L. Bloom, Zoltán Ésik
    Pages 23-45
  5. Stephen L. Bloom, Zoltán Ésik
    Pages 47-92
  6. Stephen L. Bloom, Zoltán Ésik
    Pages 93-111
  7. Stephen L. Bloom, Zoltán Ésik
    Pages 113-158
  8. Stephen L. Bloom, Zoltán Ésik
    Pages 159-213
  9. Stephen L. Bloom, Zoltán Ésik
    Pages 215-241
  10. Stephen L. Bloom, Zoltán Ésik
    Pages 243-288
  11. Stephen L. Bloom, Zoltán Ésik
    Pages 289-351
  12. Stephen L. Bloom, Zoltán Ésik
    Pages 353-447
  13. Stephen L. Bloom, Zoltán Ésik
    Pages 449-480
  14. Stephen L. Bloom, Zoltán Ésik
    Pages 481-511
  15. Stephen L. Bloom, Zoltán Ésik
    Pages 513-549
  16. Stephen L. Bloom, Zoltán Ésik
    Pages 551-611
  17. Back Matter
    Pages 612-632

About this book

Introduction

This monograph contains the results of our joint research over the last ten years on the logic of the fixed point operation. The intended au­ dience consists of graduate students and research scientists interested in mathematical treatments of semantics. We assume the reader has a good mathematical background, although we provide some prelimi­ nary facts in Chapter 1. Written both for graduate students and research scientists in theoret­ ical computer science and mathematics, the book provides a detailed investigation of the properties of the fixed point or iteration operation. Iteration plays a fundamental role in the theory of computation: for example, in the theory of automata, in formal language theory, in the study of formal power series, in the semantics of flowchart algorithms and programming languages, and in circular data type definitions. It is shown that in all structures that have been used as semantical models, the equational properties of the fixed point operation are cap­ tured by the axioms describing iteration theories. These structures include ordered algebras, partial functions, relations, finitary and in­ finitary regular languages, trees, synchronization trees, 2-categories, and others.

Keywords

Algebraische Semantik Fixed Point Theory Fixpunkttheorie Iteration Notation Programming Languages algorithms automata bisimulation computer science formal language logic programming language proof semantics

Authors and affiliations

  • Stephen L. Bloom
    • 1
  • Zoltán Ésik
    • 2
  1. 1.Department of Computer ScienceStevens Institute of TechnologyHobokenUSA
  2. 2.Department of Computer ScienceA. József UniversitySzegedHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-78034-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-78036-3
  • Online ISBN 978-3-642-78034-9
  • Series Print ISSN 1431-2654
  • Buy this book on publisher's site