This book offers a comprehensive perspective to modern topics in complexity theory, which is a central field of the theoretical foundations of computer science. It addresses the looming question of what can be achieved within a limited amount of time with or without other limited natural computational resources. Can be used as an introduction for advanced undergraduate and graduate students as either a textbook or for self-study, or to experts, since it provides expositions of the various sub-areas of complexity theory such as hardness amplification, pseudorandomness and probabilistic proof systems.
Contents
1. Introduction and preliminaries; 2. P, NP and NP-completeness; 3. Variations on P and NP; 4. More resources, more power?; 5. Space complexity; 6. Randomness and counting; 7. The bright side of hardness; 8. Pseudorandom generators; 9. Probabiistic proof systems; 10. Relaxing the requirements; Epilogue; A. Glossary of complexity classes; B. On the quest for lower bounds; C. On the foundations of modern cryptography; D. Probabilistic preliminaries and advanced topics in randomization; E. Explicit constructions; F. Some omitted proofs; G. Some computational problems.
Review
"This interesting book... is refreshing to read his [Goldreichs'] opinions... The very strong focus on conceptual issues makes the book indispensible as a reference volume for research libraries."
M. Bona, University of Florida, CHOICE
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