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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.Read more
- Contains the modern take on computational complexity as well as the classical
- Covers the basics plus advanced topics that appear for the first time in a graduate textbook
- More than 300 exercises are included
Reviews & endorsements
"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 ComputationSee more reviews
"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
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- Date Published: April 2009
- format: Hardback
- isbn: 9780521424264
- length: 594 pages
- dimensions: 259 x 185 x 38 mm
- weight: 2.78kg
- contains: 73 b/w illus. 6 tables 307 exercises
- availability: Available
Table of Contents
Part I. Basic Complexity Classes:
1. The computational model - and why it doesn't matter
2. NP and NP completeness
4. Space complexity
5. The polynomial hierarchy and alternations
6. Boolean circuits
7. Randomized computation
8. Interactive proofs
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
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.
Instructors have used or reviewed this title for the following courses
- Algorithmic Complexity
- Computer Complexity Theory
- High Performance Computing in Operations Research
- Limits of Computation
- Theory of Computation - Honors
- Theory of Computing
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