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E-grāmata: Theory of Computational Complexity 2e 2nd Edition [Wiley Online]

(University of Minnesota), (University of Houston)
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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.
Preface ix
Notes on the Second Edition xv
Part I Uniform Complexity
1(148)
1 Models of Computation and Complexity Classes
3(42)
1.1 Strings, Coding, and Boolean Functions
3(4)
1.2 Deterministic Turing Machines
7(7)
1.3 Nondeterministic Turing Machines
14(4)
1.4 Complexity Classes
18(7)
1.5 Universal Turing Machine
25(4)
1.6 Diagonalization
29(4)
1.7 Simulation
33(12)
Exercises
38(5)
Historical Notes
43(2)
2 NP-Completeness
45(36)
2.1 Np
45(4)
2.2 Cook's Theorem
49(5)
2.3 More NP-Complete Problems
54(7)
2.4 Polynomial-Time Turing Reducibility
61(7)
2.5 NP-Complete Optimization Problems
68(13)
Exercises
76(3)
Historical Notes
79(2)
3 The Polynomial-Time Hierarchy and Polynomial Space
81(38)
3.1 Nondeterministic Oracle Turing Machines
81(2)
3.2 Polynomial-Time Hierarchy
83(5)
3.3 Complete Problems in PH
88(7)
3.4 Alternating Turing Machines
95(5)
3.5 PSPACE-Complete Problems
100(8)
3.6 EXP-Complete Problems
108(11)
Exercises
114(3)
Historical Notes
117(2)
4 Structure of NP
119(30)
4.1 Incomplete Problems in NP
119(3)
4.2 One-Way Functions and Cryptography
122(7)
4.3 Relativization
129(2)
4.4 Unrelativizable Proof Techniques
131(1)
4.5 Independence Results
131(1)
4.6 Positive Relativization
132(3)
4.7 Random Oracles
135(5)
4.8 Structure of Relativized NP
140(9)
Exercises
144(3)
Historical Notes
147(2)
Part II Nonuniform Complexity
149(146)
5 Decision Trees
151(49)
5.1 Graphs and Decision Trees
151(6)
5.2 Examples
157(4)
5.3 Algebraic Criterion
161(5)
5.4 Monotone Graph Properties
166(2)
5.5 Topological Criterion
168(7)
5.6 Applications of the Fixed Point Theorems
175(4)
5.7 Applications of Permutation Groups
179(3)
5.8 Randomized Decision Trees
182(5)
5.9 Branching Programs
187(13)
Exercises
194(4)
Historical Notes
198(2)
6 Circuit Complexity
200(52)
6.1 Boolean Circuits
200(4)
6.2 Polynomial-Size Circuits
204(6)
6.3 Monotone Circuits
210(9)
6.4 Circuits with Modulo Gates
219(3)
6.5 Nc
222(6)
6.6 Parity Function
228(7)
6.7 P-Completeness
235(7)
6.8 Random Circuits and RNC
242(10)
Exercises
246(3)
Historical Notes
249(3)
7 Polynomial-Time Isomorphism
252(43)
7.1 Polynomial-Time Isomorphism
252(4)
7.2 Paddability
256(5)
7.3 Density of NP-Complete Sets
261(10)
7.4 Density of EXP-Complete Sets
271(4)
7.5 One-Way Functions and Isomorphism in EXP
275(10)
7.6 Density of P-Complete Sets
285(10)
Exercises
289(3)
Historical Notes
292(3)
Part III Probabilistic Complexity
295(163)
8 Probabilistic Machines and Complexity Classes
297(35)
8.1 Randomized Algorithms
297(5)
8.2 Probabilistic Turing Machines
302(3)
8.3 Time Complexity of Probabilistic Turing Machines
305(4)
8.4 Probabilistic Machines with Bounded Errors
309(3)
8.5 BPP and P
312(3)
8.6 BPP and NP
315(3)
8.7 BPP and the Polynomial-Time Hierarchy
318(3)
8.8 Relativized Probabilistic Complexity Classes
321(11)
Exercises
327(3)
Historical Notes
330(2)
9 Complexity of Counting
332(34)
9.1 Counting Class #P
333(3)
9.2 #P-Complete Problems
336(10)
9.3 P and the Polynomial-Time Hierarchy
346(6)
9.4 #P and the Polynomial-Time Hierarchy
352(2)
9.5 Circuit Complexity and Relativized P and #P
354(4)
9.6 Relativized Polynomial-Time Hierarchy
358(8)
Exercises
361(3)
Historical Notes
364(2)
10 Interactive Proof Systems
366(41)
10.1 Examples and Definitions
366(9)
10.2 Arthur--Merlin Proof Systems
375(4)
10.3 AM Hierarchy Versus Polynomial-Time Hierarchy
379(8)
10.4 IP Versus AM
387(9)
10.5 IP Versus PSPACE
396(11)
Exercises
402(4)
Historical Notes
406(1)
11 Probabilistically Checkable Proofs and NP-Hard Optimization Problems
407(51)
11.1 Probabilistically Checkable Proofs
407(4)
11.2 PCP Characterization of NP
411(26)
11.2.1 Expanders
414(4)
11.2.2 Gap Amplification
418(10)
11.2.3 Assignment Tester
428(9)
11.3 Probabilistic Checking and Inapproximability
437(3)
11.4 More NP-Hard Approximation Problems
440(18)
Exercises
452(3)
Historical Notes
455(3)
References 458(22)
Index 480
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.