Theory of Computational Complexity

2. Revised Auflage 2014
ISBN: 978-1-118-30608-6
Verlag: Wiley

Buch, Englisch, 512 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 933 g

Reihe: Wiley-Interscience Series in Discrete Mathematics and Optimization

Praise for the First Edition

". complete, up-to-date coverage of computational complexity theory.the book promises to become the standard reference on computational complexity."
—Zentralblatt MATH

A thorough revision based on advances in the field of computational complexity and readers’ feedback, the Second Edition of Theory of Computational Complexity presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered.

Maintaining extensive and detailed coverage, Theory of Computational Complexity, Second Edition, examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The Second Edition also features recent developments on areas such as NP-completeness theory, as well as:

- A new combinatorial proof of the PCP theorem based on the notion of expander graphs, a research area in the field of computer science
- Additional exercises at varying levels of difficulty to further test comprehension of the presented material
- End-of-chapter literature reviews that summarize each topic and offer additional sources for further study

Theory of Computational Complexity, Second Edition, is an excellent textbook for courses on computational theory and complexity at the graduate level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research.

Autoren/Hrsg.

Du, Ding-Zhu

Ko, Ker-I

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Berechenbarkeitstheorie, Komplexitätstheorie
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme

Inhaltsverzeichnis

Preface ix

Notes on the Second Edition xv

Part I Uniform Complexity 1

1 Models of Computation and Complexity Classes 3

1.1 Strings, Coding, and Boolean Functions 3

1.2 Deterministic Turing Machines 7

1.3 Nondeterministic Turing Machines 14

1.4 Complexity Classes 18

1.5 Universal Turing Machine 25

1.6 Diagonalization 29

1.7 Simulation 33

Exercises 38

Historical Notes 43

2 NP-Completeness 45

2.1 Np 45

2.2 Cook’s Theorem 49

2.3 More NP-Complete Problems 54

2.4 Polynomial-Time Turing Reducibility 61

2.5 NP-Complete Optimization Problems 68

Exercises 76

Historical Notes 79

3 The Polynomial-Time Hierarchy and Polynomial Space 81

3.1 Nondeterministic Oracle Turing Machines 81

3.2 Polynomial-Time Hierarchy 83

3.3 Complete Problems in PH 88

3.4 Alternating Turing Machines 95

3.5 PSPACE-Complete Problems 100

3.6 EXP-Complete Problems 108

Exercises 114

Historical Notes 117

4 Structure of NP 119

4.1 Incomplete Problems in NP 119

4.2 One-Way Functions and Cryptography 122

4.3 Relativization 129

4.4 Unrelativizable Proof Techniques 131

4.5 Independence Results 131

4.6 Positive Relativization 132

4.7 Random Oracles 135

4.8 Structure of Relativized NP 140

Exercises 144

Historical Notes 147

Part II Nonuniform Complexity 149

5 Decision Trees 151

5.1 Graphs and Decision Trees 151

5.2 Examples 157

5.3 Algebraic Criterion 161

5.4 Monotone Graph Properties 166

5.5 Topological Criterion 168

5.6 Applications of the Fixed Point Theorems 175

5.7 Applications of Permutation Groups 179

5.8 Randomized Decision Trees 182

5.9 Branching Programs 187

Exercises 194

Historical Notes 198

6 Circuit Complexity 200

Über Autor(innen)

DING-ZHU DU, PhD, is Professor in the Department of Computer Science at the University of Texas at Dallas. He has published over 180 journal articles in his areas of research interest, which include design and analysis of approximation algorithms for combinatorial optimization problems and communication networks. Dr. Du is also the coauthor of Problem Solving in Automata, Languages, and Complexity, also published by Wiley.
KER-I KO, PhD, is Professor in the Department of Computer Science at National Chiao Tung University, Taiwan. He has published extensively in his areas of research interest, which include computational complexity theory and its applications to numerical computation. Dr. Ko is also the coauthor of Problem Solving in Automata, Languages, and Complexity, also published by Wiley.