Computational Complexity

A Modern Approach

Nonfiction, Science & Nature, Mathematics, Discrete Mathematics, Computers, General Computing, Reference & Language, Reference
Cover of the book Computational Complexity by Sanjeev Arora, Boaz Barak, Cambridge University Press
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Author: Sanjeev Arora, Boaz Barak ISBN: 9781139234757
Publisher: Cambridge University Press Publication: April 20, 2009
Imprint: Cambridge University Press Language: English
Author: Sanjeev Arora, Boaz Barak
ISBN: 9781139234757
Publisher: Cambridge University Press
Publication: April 20, 2009
Imprint: Cambridge University Press
Language: English

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models (decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity), average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.

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This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models (decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity), average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.

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