Theory of Computational Complexity ( Wiley Series in Discrete Mathematics and Optimization )

Publication series :Wiley Series in Discrete Mathematics and Optimization

Author: Ding-Zhu Du  

Publisher: John Wiley & Sons Inc‎

Publication year: 2014

E-ISBN: 9781118593035

P-ISBN(Hardback):  9781118306086

Subject: O141 (mathematical logic) symbolic logic.

Language: ENG

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Description

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.

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 complexit

Chapter

1.3 Nondeterministic Turing Machines

1.4 Complexity Classes

1.5 Universal Turing Machine

1.6 Diagonalization

1.7 Simulation

Exercises

Historical Notes

Chapter 2 NP-Completeness

2.1 NP

2.2 Cook's Theorem

2.3 More NP-Complete Problems

2.4 Polynomial-Time Turing Reducibility

2.5 NP-Complete Optimization Problems

Exercises

Historical Notes

Chapter 3 The Polynomial-Time Hierarchy and Polynomial Space

3.1 Nondeterministic Oracle Turing Machines

3.2 Polynomial-Time Hierarchy

3.3 Complete Problems in PH

3.4 Alternating Turing Machines

3.5 PSPACE-Complete Problems

3.6 EXP-Complete Problems

Exercises

Historical Notes

Chapter 4 Structure of NP

4.1 Incomplete Problems in NP

4.2 One-Way Functions and Cryptography

4.3 Relativization

4.4 Unrelativizable Proof Techniques

4.5 Independence Results

4.6 Positive Relativization

4.7 Random Oracles

4.8 Structure of Relativized NP

Exercises

Historical Notes

Part II Nonuniform Complexity

Chapter 5 Decision Trees

5.1 Graphs and Decision Trees

5.2 Examples

5.3 Algebraic Criterion

5.4 Monotone Graph Properties

5.5 Topological Criterion

5.6 Applications of the Fixed Point Theorems

5.7 Applications of Permutation Groups

5.8 Randomized Decision Trees

5.9 Branching Programs

Exercises

Historical Notes

Chapter 6 Circuit Complexity

6.1 Boolean Circuits

6.2 Polynomial-Size Circuits

6.3 Monotone Circuits

6.4 Circuits with Modulo Gates

6.5 NC

6.6 Parity Function

6.7 P-Completeness

6.8 Random Circuits and RNC

Exercises

Historical Notes

Chapter 7 Polynomial-Time Isomorphism

7.1 Polynomial-Time Isomorphism

7.2 Paddability

7.3 Density of NP-Complete Sets

7.4 Density of EXP-Complete Sets

7.5 One-Way Functions and Isomorphism in EXP

7.6 Density of P-Complete Sets

Exercises

Historical Notes

Part III Probabilistic Complexity

Chapter 8 Probabilistic Machines and Complexity Classes

8.1 Randomized Algorithms

8.2 Probabilistic Turing Machines

8.3 Time Complexity of Probabilistic Turing Machines

8.4 Probabilistic Machines with Bounded Errors

8.5 BPP and P

8.6 BPP and NP

8.7 BPP and the Polynomial-Time Hierarchy

8.8 Relativized Probabilistic Complexity Classes

Exercises

Historical Notes

Chapter 9 Complexity of Counting

9.1 Counting Class #P

9.2 #P-Complete Problems

9.3 oplus P and the Polynomial-Time Hierarchy

9.4 #P and the Polynomial-Time Hierarchy

9.5 Circuit Complexity and Relativized oplus P and #P

9.6 Relativized Polynomial-Time Hierarchy

Exercises

Historical Notes

Chapter 10 Interactive Proof Systems

10.1 Examples and Definitions

10.2 Arthur-Merlin Proof Systems

10.3 AM Hierarchy Versus Polynomial-Time Hierarchy

10.4 IP Versus AM

10.5 IP Versus PSPACE

Exercises

Historical Notes

Chapter 11 Probabilistically Checkable Proofs and NP-Hard Optimization Problems

11.1 Probabilistically Checkable Proofs

11.2 PCP Characterization of NP

11.2.1 Expanders

11.2.2 Gap Amplification

11.2.3 Assignment Tester

11.3 Probabilistic Checking and Inapproximability

11.4 More NP-Hard Approximation Problems

Exercises

Historical Notes

References

Index

Wiley Series in Discrete Mathematics and Optimization

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