计算复杂性的现代方法

内容简介

《计算复杂性的现代方法》是一部将所有有关复杂度知识理论集于一体的教程。将进展和经典结果结合起来，是一部很难得的研究生入门级教程。既是相关科研人员的一部很好的参考书，也是自学人员很难得的一本很好自学教程。本书一开始引入该领域的本知识，然后逐步深入，介绍更多深层次的结果，每章末都附有练习。对复杂度感兴趣的人士，物理学家，数学家以及科研人员这本书都是相当受益。

目录

about this bOok
Acknowledgments
Introduction
0 Notational conventions

PARTONE: 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 TWO: LOWER BOUNDS FOR ConCRETE COMPUTATIonAL MODELS
12 Decision trees
13 Communication complexity
14 Circuit lower bounds: Complexity theory's Waterloo
15 Proof complexity
16 Algebraic computation models

PART THREE: 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: Mathematical background
Hints and selected exercises
Main theorems and definitions
Bibliography
Index
Complexity class index