Computational Complexity: A Quantitative Perspective - 1st Edition - ISBN: 9780444828415, 9780080476667

Computational Complexity: A Quantitative Perspective, Volume 196

1st Edition

Authors: Marius Zimand
eBook ISBN: 9780080476667
Hardcover ISBN: 9780444828415
Imprint: Elsevier Science
Published Date: 7th July 2004
Page Count: 352
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Table of Contents

Contents Preface.

  1. Preliminaries.

  2. Abstract complexity theory.

  3. P, NP, and E.

  4. Quantum computation.

  5. One-way functions, pseudo-random generators.

  6. Optimization problems.

A. Tail bounds.




There has been a common perception that computational complexity is a theory of "bad news" because its most typical results assert that various real-world and innocent-looking tasks are infeasible. In fact, "bad news" is a relative term, and, indeed, in some situations (e.g., in cryptography), we want an adversary to not be able to perform a certain task. However, a "bad news" result does not automatically become useful in such a scenario. For this to happen, its hardness features have to be quantitatively evaluated and shown to manifest extensively.

The book undertakes a quantitative analysis of some of the major results in complexity that regard either classes of problems or individual concrete problems. The size of some important classes are studied using resource-bounded topological and measure-theoretical tools. In the case of individual problems, the book studies relevant quantitative attributes such as approximation properties or the number of hard inputs at each length.

One chapter is dedicated to abstract complexity theory, an older field which, however, deserves attention because it lays out the foundations of complexity. The other chapters, on the other hand, focus on recent and important developments in complexity. The book presents in a fairly detailed manner concepts that have been at the centre of the main research lines in complexity in the last decade or so, such as: average-complexity, quantum computation, hardness amplification, resource-bounded measure, the relation between one-way functions and pseudo-random generators, the relation between hard predicates and pseudo-random generators, extractors, derandomization of bounded-error probabilistic algorithms, probabilistically checkable proofs, non-approximability of optimization problems, and others.

The book should appeal to graduate computer science students, and to researchers who have an interest in computer science theory and need a good understanding of computational complexity, e.g., researchers in algorithms, AI, logic, and other disciplines.

Key Features

· Emphasis is on relevant quantitative attributes of important results in complexity. · Coverage is self-contained and accessible to a wide audience. · Large range of important topics including: derandomization techniques, non-approximability of optimization problems, average-case complexity, quantum computation, one-way functions and pseudo-random generators, resource-bounded measure and topology.


University libraries, researchers in the field theory of computation, computational complexity, algorithms, and al graduate students in computer science.


No. of pages:
© Elsevier Science 2004
Elsevier Science
eBook ISBN:
Hardcover ISBN:


"This book analyzes quantitative aspects of some of the most important results in computational complexity. It will benefit most the reader who already knows the basic tenets of complexity and wants to find out more about it than what is covered in standard courses." --Gerhard Lischke

About the Authors

Marius Zimand Author

Affiliations and Expertise

Townson University, Townson, USA.