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.
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Sanjeev Arora is a Professor in the department of computer science at Princeton University. He holds a Ph.D. from the University of California, Berkeley and has done foundational work in complexity theory, probabilistically checkable proofs, and approximation algorithms. Boaz Barak is an assistant professor in the department of computer science at Princeton University. He holds a Ph.D. from the Weizmann Institute of Science.
'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
'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, author of Introduction to the Theory of
Computation
'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
 |
Ask a Question About this Product More... |
|
