Computational Complexity A Modern Approach [Hardcover]

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory, including interactive proofs, PCP, derandomization, and quantum computation. It can be used as a reference, for self-study, or as a textbook. More than 300 exercises are included.This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory, including interactive proofs, PCP, derandomization, and quantum computation. It can be used as a reference, for self-study, or as a textbook. More than 300 exercises are included.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.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 lS¯