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9780521424264

Computational Complexity : A Modern Approach

by
  • ISBN13:

    9780521424264

  • ISBN10:

    0521424267

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2009-04-20
  • Publisher: Cambridge University Press

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Supplemental Materials

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Summary

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.

Table of Contents

Basic Complexity Classes
The computational model - and why it doesn't matter
NP and NP completeness
Diagonalization
Space complexity
The polynomial hierarchy and alternations
Boolean circuits
Randomized computation
Interactive proofs
Cryptography
Quantum computation
PCP theorem and hardness of approximation: an introduction
Lower Bounds for Concrete Computational Models
Decision trees
Communication complexity
Circuit lower bounds
Proof complexity
Algebraic computation models
Advanced Topics
Complexity of counting
Average case complexity: Levin's theory
Hardness amplification and error correcting codes
Derandomization
Pseudorandom constructions: expanders and extractors
Proofs of PCP theorems and the Fourier transform technique
Why are circuit lower bounds so difficult?
mathematical background
Table of Contents provided by Publisher. All Rights Reserved.

Supplemental Materials

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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