Computational Complexity
A Modern Approach

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Sanjeev Arora (Author), Boaz Barak (Author)

9780521424264, Cambridge University Press

Hardback, published 20 April 2009

594 pages, 73 b/w illus. 6 tables 307 exercises
25.9 x 18.5 x 3.8 cm, 2.78 kg

'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 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.

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.

Subject Areas: Mathematical theory of computation [UYA], Coding theory & cryptology [GPJ]