Logic and Complexity

  • Richard Lassaigne
  • Michel de Rougemont

Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Introduction

    1. Richard Lassaigne, Michel de Rougemont
      Pages 1-2
  3. Basic model theory and computability

    1. Front Matter
      Pages 3-3
    2. Richard Lassaigne, Michel de Rougemont
      Pages 5-23
    3. Richard Lassaigne, Michel de Rougemont
      Pages 25-39
    4. Richard Lassaigne, Michel de Rougemont
      Pages 41-55
    5. Richard Lassaigne, Michel de Rougemont
      Pages 57-66
    6. Richard Lassaigne, Michel de Rougemont
      Pages 67-82
    7. Richard Lassaigne, Michel de Rougemont
      Pages 83-108
    8. Richard Lassaigne, Michel de Rougemont
      Pages 109-128
  4. Descriptive Complexity

    1. Front Matter
      Pages 129-129
    2. Richard Lassaigne, Michel de Rougemont
      Pages 131-150
    3. Richard Lassaigne, Michel de Rougemont
      Pages 151-174
    4. Richard Lassaigne, Michel de Rougemont
      Pages 175-190
    5. Richard Lassaigne, Michel de Rougemont
      Pages 191-212
    6. Richard Lassaigne, Michel de Rougemont
      Pages 213-227
    7. Richard Lassaigne, Michel de Rougemont
      Pages 229-250
    8. Richard Lassaigne, Michel de Rougemont
      Pages 251-262
  5. Approximation and classes beyond NP

    1. Front Matter
      Pages 263-263
    2. Richard Lassaigne, Michel de Rougemont
      Pages 265-277

About this book

Introduction

Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems.

Divided into three parts, it covers:

- Model Theory and Recursive Functions - introducing the basic model theory of propositional, 1st order, inductive definitions and 2nd order logic. Recursive functions, Turing computability and decidability are also examined.

- Descriptive Complexity - looking at the relationship between definitions of problems, queries, properties of programs and their computational complexity.

- Approximation - explaining how some optimization problems and counting problems can be approximated according to their logical form.

Logic is important in Computer Science, particularly for verification problems and database query languages such as SQL. Students and researchers in this field will find this book of great interest.

Keywords

Computer SQL algorithm algorithms complexity complexity theory computer science database logic mathematical logic model theory optimization verification

Authors and affiliations

  • Richard Lassaigne
    • 1
  • Michel de Rougemont
    • 2
  1. 1.Maitre de ConferencesUniversity Paris VIIFrance
  2. 2.University Paris IIFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-392-3
  • Copyright Information Springer-Verlag London 2004
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4471-1052-1
  • Online ISBN 978-0-85729-392-3
  • About this book