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Iteration Theories

The Equational Logic of Iterative Processes

  • Book
  • © 1993

Overview

Authors:
  1. Stephen L. Bloom

    1. Department of Computer Science, Stevens Institute of Technology, Hoboken, USA

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  2. Zoltán Ésik

    1. Department of Computer Science, A. József University, Szeged, Hungary

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    • Stephen L. Bloom, Zoltán Ésik
    Pages 1-6

  3. Preliminary Facts

    • Stephen L. Bloom, Zoltán Ésik
    Pages 7-21

  4. Varieties and Theories

    • Stephen L. Bloom, Zoltán Ésik
    Pages 23-45

  5. Theory Facts

    • Stephen L. Bloom, Zoltán Ésik
    Pages 47-92

  6. Algebras

    • Stephen L. Bloom, Zoltán Ésik
    Pages 93-111

  7. Iterative Theories

    • Stephen L. Bloom, Zoltán Ésik
    Pages 113-158

  8. Iteration Theories

    • Stephen L. Bloom, Zoltán Ésik
    Pages 159-213

  9. Iteration Algebras

    • Stephen L. Bloom, Zoltán Ésik
    Pages 215-241

  10. Continuous Theories

    • Stephen L. Bloom, Zoltán Ésik
    Pages 243-288

  11. Matrix Iteration Theories

    • Stephen L. Bloom, Zoltán Ésik
    Pages 289-351

  12. Matricial Iteration Theories

    • Stephen L. Bloom, Zoltán Ésik
    Pages 353-447

  13. Presentations

    • Stephen L. Bloom, Zoltán Ésik
    Pages 449-480

  14. Flowchart Behaviors

    • Stephen L. Bloom, Zoltán Ésik
    Pages 481-511

  15. Synchronization Trees

    • Stephen L. Bloom, Zoltán Ésik
    Pages 513-549

  16. Floyd-Hoare Logic

    • Stephen L. Bloom, Zoltán Ésik
    Pages 551-611

  17. Back Matter

    Pages 612-632
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Computer Science, Stevens Institute of Technology, Hoboken, USA

    Stephen L. Bloom

  • Department of Computer Science, A. József University, Szeged, Hungary

    Zoltán Ésik

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