計(jì)算復(fù)雜性的現(xiàn)代方法簡介，目錄書摘
2019-12-20 14:17
來源：京東
作者：京東
計(jì)算復(fù)雜性的現(xiàn)代方法
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內(nèi)容簡介: 《計(jì)算復(fù)雜性的現(xiàn)代方法》是一部將所有有關(guān)復(fù)雜度知識(shí)理論集于一體的教程。將最新進(jìn)展和經(jīng)典結(jié)果結(jié)合起來，是一部很難得的研究生入門級(jí)教程。既是相關(guān)科研人員的一部很好的參考書，也是自學(xué)人員很難得的一本很好自學(xué)教程。本書一開始引入該領(lǐng)域的最基本知識(shí)，然后逐步深入，介紹更多深層次的結(jié)果，每章末都附有練習(xí)。對復(fù)雜度感興趣的人士，物理學(xué)家，數(shù)學(xué)家以及科研人員這本書都是相當(dāng)受益。
作者簡介:
目錄: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
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
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