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    Computational Complexity: A Modern Approach (Hardback) By (author) Sanjeev Arora, By (author) Boaz Barak

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    DescriptionThis 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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  • Full bibliographic data for Computational Complexity

    Title
    Computational Complexity
    Subtitle
    A Modern Approach
    Authors and contributors
    By (author) Sanjeev Arora, By (author) Boaz Barak
    Physical properties
    Format: Hardback
    Number of pages: 594
    Width: 215 mm
    Height: 253 mm
    Thickness: 35 mm
    Weight: 1,210 g
    Language
    English
    ISBN
    ISBN 13: 9780521424264
    ISBN 10: 0521424267
    Classifications

    BIC E4L: COM
    Nielsen BookScan Product Class 3: S10.0
    B&T Book Type: NF
    B&T Modifier: Region of Publication: 01
    Warengruppen-Systematik des deutschen Buchhandels: 16320
    BIC subject category V2: GPJ
    B&T Modifier: Academic Level: 02
    LC subject heading:
    B&T Modifier: Text Format: 06
    B&T General Subject: 229
    B&T Modifier: Text Format: 01
    BIC subject category V2: UYA
    Ingram Subject Code: XG
    BISAC V2.8: COM000000
    B&T Merchandise Category: UP
    BISAC V2.8: MAT018000
    LC subject heading:
    DC22: 511.3/52, 511.352
    LC classification: QA267.7 .A76 2009
    Edition
    1
    Illustrations note
    73 b/w illus. 6 tables 307 exercises
    Publisher
    CAMBRIDGE UNIVERSITY PRESS
    Imprint name
    CAMBRIDGE UNIVERSITY PRESS
    Publication date
    01 June 2009
    Publication City/Country
    Cambridge
    Author Information
    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 is an assistant professor in the department of computer science at Princeton University. He holds a Ph.D. from the Weizmann Institute of Science.
    Review quote
    '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
    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.