Computational Complexity: A Modern Approach

by Sanjeev Arora, Boaz Barak

Overview

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models (decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity), average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.

Product Details

ISBN-13:	9781139234757
Publisher:	Cambridge University Press
Publication date:	04/20/2009
Sold by:	Barnes & Noble
Format:	eBook
File size:	21 MB
Note:	This product may take a few minutes to download.

About the Author

Sanjeev Arora is a Professor in the department of computer science at Princeton University. He holds a Ph.D. from the University of California, Berkeley and has done foundational work in complexity theory, probabilistically checkable proofs, and approximation algorithms.
Boaz Barak is an assistant professor in the department of computer science at Princeton University. He holds a Ph.D. from the Weizmann Institute of Science.

Table of Contents

Part I. Basic Complexity Classes: 1. The computational model - and why it doesn't matter; 2. NP and NP completeness; 3. Diagonalization; 4. Space complexity; 5. The polynomial hierarchy and alternations; 6. Boolean circuits; 7. Randomized computation; 8. Interactive proofs; 9. Cryptography; 10. Quantum computation; 11. PCP theorem and hardness of approximation: an introduction; Part II. Lower Bounds for Concrete Computational Models: 12. Decision trees; 13. Communication complexity; 14. Circuit lower bounds; 15. Proof complexity; 16. Algebraic computation models; Part III. Advanced Topics: 17. Complexity of counting; 18. Average case complexity: Levin's theory; 19. Hardness amplification and error correcting codes; 20. Derandomization; 21. Pseudorandom constructions: expanders and extractors; 22. Proofs of PCP theorems and the Fourier transform technique; 23. Why are circuit lower bounds so difficult?; Appendix A: mathematical background.

Editorial Reviews

"This text is a major achievement that brings together all of the important developments in complexity theory. Student and researchers alike will find it to be an immensely useful resource."
Michael Sipser, MIT, author of Introduction to the Theory of Computation


"Computational complexity theory is at the core of theoretical computer science research. This book contains essentially all of the (many) exciting developments of the last two decades, with high level intuition and detailed technical proofs. It is a must for everyone interested in this field."
Avi Wigderson, Professor, Institute for Advanced Study, Princeton

"This book by two leading theoretical computer scientists provides a comprehensive,insightful and mathematically precise overview of computational complexity theory, ranging from early foundational work to emerging areas such as quantum computation and hardness of approximation. It will serve the needs of a wide audience, ranging from experienced researchers to graduate students and ambitious undergraduates seeking an introduction to the mathematical foundations of computer science. I will keep it at my side as a useful reference for my own teaching and research."
Richard M. Karp, University Professor, University of California at Berkeley

"The reviewer's impressions are that this new textbook on computational complexity is available for a very attractive price and that on Amazon it may be verified that it has received very good reviews by several leaders in this field (Karp, Sipser, Wigderson)."
Ulrich Tamm, Mathematical Reviews

From the Publisher