Limits of Computation

From a Programming Perspective

  • Bernhard┬áReus

Part of the Undergraduate Topics in Computer Science book series (UTICS)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Bernhard Reus
    Pages 1-9
  3. Computability

    1. Front Matter
      Pages 11-11
    2. Bernhard Reus
      Pages 13-28
    3. Bernhard Reus
      Pages 29-45
    4. Bernhard Reus
      Pages 47-54
    5. Bernhard Reus
      Pages 55-63
    6. Bernhard Reus
      Pages 65-70
    7. Bernhard Reus
      Pages 71-86
    8. Bernhard Reus
      Pages 87-96
    9. Bernhard Reus
      Pages 97-112
    10. Bernhard Reus
      Pages 113-121
    11. Bernhard Reus
      Pages 123-148
  4. Complexity

    1. Front Matter
      Pages 149-149
    2. Bernhard Reus
      Pages 151-160
    3. Bernhard Reus
      Pages 161-171
    4. Bernhard Reus
      Pages 173-181
    5. Bernhard Reus
      Pages 183-194
    6. Bernhard Reus
      Pages 195-216
    7. Bernhard Reus
      Pages 217-226

About this book

Introduction

This textbook discusses the most fundamental and puzzling questions about the foundations of computing. In 23 lecture-sized chapters it provides an exciting tour through the most important results in the field of computability and time complexity, including the Halting Problem, Rice's Theorem, Kleene's Recursion Theorem, the Church-Turing Thesis, Hierarchy Theorems, and Cook-Levin's Theorem. Each chapter contains classroom-tested material, including examples and exercises. Links between adjacent chapters provide a coherent narrative.

Fundamental results are explained lucidly by means of programs written in a simple, high-level imperative programming language, which only requires basic mathematical knowledge. Throughout the book, the impact of the presented results on the entire field of computer science is emphasised. Examples range from program analysis to networking, from database programming to popular games and puzzles.  Numerous biographical footnotes about the famous scientists who developed the subject are also included.

"Limits of Computation" offers a thorough, yet accessible, introduction to computability and complexity for the computer science student of the 21st century.

Keywords

Computability Computational Complexity Fixpoint Theorem Halting Problem Graph Theory

Authors and affiliations

  • Bernhard┬áReus
    • 1
  1. 1.Department of InformaticsUniversity of SussexBrightonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-27889-6
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-27887-2
  • Online ISBN 978-3-319-27889-6
  • Series Print ISSN 1863-7310
  • Series Online ISSN 2197-1781
  • About this book
Industry Sectors
Electronics
Telecommunications
Energy, Utilities & Environment
Biotechnology