Computational Complexity: A Conceptual Perspective (Google eBook)

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Cambridge University Press, Apr 28, 2008 - Computers
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Complexity theory is a central field of the theoretical foundations of computer science. It is concerned with the general study of the intrinsic complexity of computational tasks; that is, it addresses the question of what can be achieved within limited time (and/or with other limited natural computational resources). This book offers a conceptual perspective on complexity theory. It is intended to serve as an introduction for advanced undergraduate and graduate students, either as a textbook or for self-study. The book will also be useful to experts, since it provides expositions of the various sub-areas of complexity theory such as hardness amplification, pseudorandomness and probabilistic proof systems. In each case, the author starts by posing the intuitive questions that are addressed by the sub-area and then discusses the choices made in the actual formulation of these questions, the approaches that lead to the answers, and the ideas that are embedded in these answers.
  

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Contents

1 Introduction and Preliminaries
1
2 P NP and NPCompleteness
44
3 Variations on P and NP
108
4 More Resources More Power?
127
5 Space Complexity
143
6 Randomness and Counting
184
7 The Bright Side of Hardness
241
8 Pseudorandom Generators
284
A Glossary of Complexity Classes
463
B On the Quest for Lower Bounds
469
C On the Foundations of Modern Cryptography
482
D Probabilistic Preliminaries and Advanced Topics in Randomization
523
E Explicit Constructions
545
F Some Omitted Proofs
566
G Some Computational Problems
583
Bibliography
589

9 Probabilistic Proof Systems
349
10 Relaxing the Requirements
416
Epilogue
461
Index
601
Copyright

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About the author (2008)

Oded Goldreich is a Professor of Computer Science at the Weizmann Institute of Science and an Incumbent of the Meyer W. Weisgal Professorial Chair. He is an editor for the SIAM Journal on Computing, the Journal of Cryptology, and Computational Complexity and previously authored the books Modern Cryptography, Probabalistic Proofs and Pseudorandomness and the two-volume work Foundations of Cryptography.

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