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Computability and Complexity Theory

  • Steven Homer
  • Alan L. Selman
Textbook

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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Steven Homer, Alan L. Selman
    Pages 1-21
  3. Steven Homer, Alan L. Selman
    Pages 23-40
  4. Steven Homer, Alan L. Selman
    Pages 41-73
  5. Steven Homer, Alan L. Selman
    Pages 75-80
  6. Steven Homer, Alan L. Selman
    Pages 81-122
  7. Steven Homer, Alan L. Selman
    Pages 123-144
  8. Steven Homer, Alan L. Selman
    Pages 145-179
  9. Steven Homer, Alan L. Selman
    Pages 181-199
  10. Steven Homer, Alan L. Selman
    Pages 201-223
  11. Steven Homer, Alan L. Selman
    Pages 225-246
  12. Steven Homer, Alan L. Selman
    Pages 247-260
  13. Steven Homer, Alan L. Selman
    Pages 261-282
  14. Back Matter
    Pages 283-298

About this book

Introduction

This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations.  Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable.  Substantial new content in this edition includes:

  • a chapter on nonuniformity studying Boolean circuits, advice classes and the important result of Karp─Lipton.
  • a chapter studying properties of the fundamental probabilistic complexity classes
  • a study of the alternating Turing machine and uniform circuit classes.
  • an introduction of counting classes, proving the famous results of Valiant and Vazirani and of Toda
  • a thorough treatment of the proof that IP is identical to PSPACE

With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool.

 

Topics and features:

  • Concise, focused  materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes
  • Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner
  • Provides key mathematical background information, including sections on logic and number theory and algebra
  • Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes

Keywords

Computability NP-Completeness Nondeterminism Nonuniform Complexity Parallelism computational complexity counting classes interactive proof systems probabilistic complexity classes relative computability undecidability

Authors and affiliations

  • Steven Homer
    • 1
  • Alan L. Selman
    • 2
  1. 1., Computer Science DepartmentBoston UniversityBostonUSA
  2. 2.The State University of New York, Department of Computer ScienceUniversity at BuffaloBuffaloUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-0682-2
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, Boston, MA
  • eBook Packages Computer Science
  • Print ISBN 978-1-4614-0681-5
  • Online ISBN 978-1-4614-0682-2
  • Series Print ISSN 1868-0941
  • Series Online ISSN 1868-095X
  • Buy this book on publisher's site
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