Sanjeev Arora, Boaz BarakCambridge University Press, 4/20/2009EAN 9780521424264, ISBN10: 0521424267Hardcover, 594 pages, 25.9 x 18.5 x 3.8 cmLanguage: EnglishThis 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 Classes1. The computational model - and why it doesn't matter2. NP and NP completeness3. Diagonalization4. Space complexity5. The polynomial hierarchy and alternations6. Boolean circuits7. Randomized computation8. Interactive proofs9. Cryptography10. Quantum computation11. PCP theorem and hardness of approximationan introductionPart II. Lower Bounds for Concrete Computational Models12. Decision trees13. Communication complexity14. Circuit lower bounds15. Proof complexity16. Algebraic computation modelsPart III. Advanced Topics17. Complexity of counting18. Average case complexityLevin's theory19. Hardness amplification and error correcting codes20. Derandomization21. Pseudorandom constructionsexpanders and extractors22. Proofs of PCP theorems and the Fourier transform technique23. Why are circuit lower bounds so difficult?Appendix Amathematical 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
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