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Descriptive Complexity

  • Textbook
  • © 1999

Overview

Authors:
  1. Neil Immerman

    1. Department of Computer Science, University of Massachusetts, Amherst, USA

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  • Self-contained introduction to a fundamental area in computer science Provides readers with an understanding of logic and complexity Explores applications and future directions Includes numerous examples and exercises to further illustrate the ideas presented This subject has important applications to databases such as analyzing the queries computable in polynomial time, analyzing the parallel time needed to compute a query, and the analysis of nondeterministic classes

Part of the book series: Texts in Computer Science (TCS)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introduction

    • Neil Immerman
    Pages 1-3

  3. Background in Logic

    • Neil Immerman
    Pages 5-22

  4. Background in Complexity

    • Neil Immerman
    Pages 23-43

  5. First-Order Reductions

    • Neil Immerman
    Pages 45-55

  6. Inductive Definitions

    • Neil Immerman
    Pages 57-66

  7. Parallelism

    • Neil Immerman
    Pages 67-89

  8. Ehrenfeucht-Fraïssé Games

    • Neil Immerman
    Pages 91-112

  9. Second-Order Logic and Fagin’s Theorem

    • Neil Immerman
    Pages 113-124

  10. Second-Order Lower Bounds

    • Neil Immerman
    Pages 125-137

  11. Complementation and Transitive Closure

    • Neil Immerman
    Pages 139-155

  12. Polynomial Space

    • Neil Immerman
    Pages 157-168

  13. Uniformity and Precomputation

    • Neil Immerman
    Pages 169-180

  14. The Role of Ordering

    • Neil Immerman
    Pages 181-202

  15. Lower Bounds

    • Neil Immerman
    Pages 203-219

  16. Applications

    • Neil Immerman
    Pages 221-240

  17. Conclusions and Future Directions

    • Neil Immerman
    Pages 241-250

  18. Back Matter

    Pages 251-268
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Keywords

About this book

A basic issue in computer science is the complexity of problems. Computational complexity measures how much time or memory is needed as a function of the input problem size. Descriptive complexity is concerned with problems which may be described in first-order logic. By virtue of the close relationship between logic and relational databses, it turns out that this subject has important applications to databases such as analysing the queries computable in polynomial time, analysing the parallel time needed to compute a query, and the analysis of nondeterministic classes. This book is written as a graduate text and so aims to provide a reasonably self-contained introduction to this subject. The author has provided numerous examples and exercises to further illustrate the ideas presented.

Authors and Affiliations

  • Department of Computer Science, University of Massachusetts, Amherst, USA

    Neil Immerman

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