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Theory of Computational Complexity

Ding-Zhu Du, Ker-I Ko

ISBN: 978-1-118-03291-6 December 2013 512 Pages



A complete treatment of fundamentals and recent advances in complexity theory Complexity theory studies the inherent difficulties of solving algorithmic problems by digital computers. This comprehensive work discusses the major topics in complexity theory, including fundamental topics as well as recent breakthroughs not previously available in book form. Theory of Computational Complexity offers a thorough presentation of the fundamentals of complexity theory, including NP-completeness theory, the polynomial-time hierarchy, relativization, and the application to cryptography. It also examines the theory of nonuniform computational complexity, including the computational models of decision trees and Boolean circuits, and the notion of polynomial-time isomorphism. The theory of probabilistic complexity, which studies complexity issues related to randomized computation as well as interactive proof systems and probabilistically checkable proofs, is also covered. Extraordinary in both its breadth and depth, this volume:
* Provides complete proofs of recent breakthroughs in complexity theory
* Presents results in well-defined form with complete proofs and numerous exercises
* Includes scores of graphs and figures to clarify difficult material
An invaluable resource for researchers as well as an important guide for graduate and advanced undergraduate students, Theory of Computational Complexity is destined to become the standard reference in the field.

Models of Computation and Complexity Classes.


The Polynomial-Time Hierarchy and Polynomial Space.

Structure of NP.


Decision Trees.

Circuit Complexity.

Polynomial-Time Isomorphism.


Probabilistic Machines and Complexity Classes.

Complexity of Counting.

Interactive Proof Systems.

Probabilistically Checkable Proofs and NP-Hard Optimization Problems.


"Here one finds both a basic introduction and comprehensive treatments, especially of topics that have borne spectacular fruit in just the last few years..." (Choice, Vol. 38, No. 10, June 2001)

"Graduate students in this area of computer science will simply find htis book indispensable." (CHOICE, June 2001)

"Du and Ko present the fundamentals of complexity theory, including NP-completeness theory, the polynomial-time hierarchy, relativization..." (SciTech Book News, Vol. 24, No. 4, December 2000)

Overall, I would recommend this book as an excellent addition to the literature. (Bulleting of the London Mathematical Society, Volume 33, 2001)

"The a graduate text...however, it can also be used profitably by researchers in theory...the selection by the authors of the book under review is excellent." (Mathematical Reviews, Issue 2001k)

Excerpt from publisher's description: "...promises to become the standard reference on computational complexity." (Zentralblatt MATH, Vol. 963, 2001/13)

"the book promises to become the standard reference on computational complexity" (Zentralblatt MATH, Vol.963, No.13 2001)