COMPUTATIONAL COMPLEXITY: A MODERN APPROACH

定價：~~1200~~ 元

NT $ 140 ~ 1,140

作者：ARORA
出版社：全華圖書
出版日期：2009-01-01
語言：繁體中文
ISBN10：0521424267
ISBN13：9780521424264
裝訂：精裝 / 608頁 / 普通級 / 單色印刷 / 初版

內容簡介

　　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.

Part I. Basic Complexity Classes:
Ch 1. The computational model - and why it doesn't matter
Ch 2. NP and NP completeness
Ch 3. Diagonalization
Ch 4. Space complexity
Ch 5. The polynomial hierarchy and alternations
Ch 6. Boolean circuits
Ch 7. Randomized computation
Ch 8. Interactive proofs
Ch 9. Cryptography
Ch 10. Quantum computation
Ch 11. PCP theorem and hardness of approximation: an introduction

Part II. Lower Bounds for Concrete Computational Models:
Ch 12. Decision trees
Ch 13. Communication complexity
Ch 14. Circuit lower bounds
Ch 15. Proof complexity
Ch 16. Algebraic computation models

Part III. Advanced Topics:
Ch 17. Complexity of counting
Ch 18. Average case complexity: Levin's theory
Ch 19. Hardness amplification and error correcting codes
Ch 20. Derandomization
Ch 21. Pseudorandom constructions: expanders and extractor
Ch 22. Proofs of PCP theorems and the Fourier transform technique
Ch 23. Why are circuit lower bounds so difficult?Appendix A: mathematical background.

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