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Computational Complexity
A Modern Approach


  • Date Published: June 2009
  • availability: Available
  • format: Hardback
  • isbn: 9780521424264

£ 46.99

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About the Authors
  • 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.

    • Contains the modern take on computational complexity as well as the classical
    • Covers the basics plus advanced topics that appear for the first time in a graduate textbook
    • More than 300 exercises are included
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    Reviews & endorsements

    'This book by two leading theoretical computer scientists provides a comprehensive, insightful and mathematically precise overview of computational complexity theory, ranging from early foundational work to emerging areas such as quantum computation and hardness of approximation. It will serve the needs of a wide audience, ranging from experienced researchers to graduate students and ambitious undergraduates seeking an introduction to the mathematical foundations of computer science. I will keep it at my side as a useful reference for my own teaching and research.' Richard M. Karp, University of California at Berkeley

    'This text is a major achievement that brings together all of the important developments in complexity theory. Student and researchers alike will find it to be an immensely useful resource.' Michael Sipser, author of Introduction to the Theory of Computation

    'Computational complexity theory is at the core of theoretical computer science research. This book contains essentially all of the (many) exciting developments of the last two decades, with high level intuition and detailed technical proofs. It is a must for everyone interested in this field.' Avi Wigderson, Professor, Institute for Advanced Study, Princeton

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    Product details

    • Date Published: June 2009
    • format: Hardback
    • isbn: 9780521424264
    • length: 594 pages
    • dimensions: 259 x 185 x 38 mm
    • weight: 2.78kg
    • contains: 73 b/w illus. 6 tables 307 exercises
    • availability: Available
  • Table of Contents

    Part I. Basic Complexity Classes:
    1. The computational model - and why it doesn't matter
    2. NP and NP completeness
    3. Diagonalization
    4. Space complexity
    5. The polynomial hierarchy and alternations
    6. Boolean circuits
    7. Randomized computation
    8. Interactive proofs
    9. Cryptography
    10. Quantum computation
    11. PCP theorem and hardness of approximation: an introduction
    Part II. Lower Bounds for Concrete Computational Models:
    12. Decision trees
    13. Communication complexity
    14. Circuit lower bounds
    15. Proof complexity
    16. Algebraic computation models
    Part III. Advanced Topics:
    17. Complexity of counting
    18. Average case complexity: Levin's theory
    19. Hardness amplification and error correcting codes
    20. Derandomization
    21. Pseudorandom constructions: expanders and extractors
    22. Proofs of PCP theorems and the Fourier transform technique
    23. Why are circuit lower bounds so difficult?
    Appendix A: mathematical background.

  • Instructors have used or reviewed this title for the following courses

    • Algorithmic Complexity
    • Computer Complexity Theory
    • Cryptography
    • High Performance Computing in Operations Research
    • Limits of Computation
    • Theory of Computation - Honors
    • Theory of Computing
  • Authors

    Sanjeev Arora, Princeton University, New Jersey
    Sanjeev Arora is a Professor in the department of computer science at Princeton University. He holds a Ph.D. from the University of California, Berkeley and has done foundational work in complexity theory, probabilistically checkable proofs, and approximation algorithms.

    Boaz Barak, Princeton University, New Jersey
    Boaz Barak is an assistant professor in the department of computer science at Princeton University. He holds a Ph.D. from the Weizmann Institute of Science.

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