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.
Autorentext
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.Klappentext
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.
Zusammenfassung
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.
Inhalt
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 Relativ…