Computational Complexity: A Modern Approach
Cambridge University Press, 4/20/2009
EAN 9780521424264, ISBN10: 0521424267
Hardcover, 594 pages, 25.9 x 18.5 x 3.8 cm
Language: English
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.
'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 of California at Berkeley