Written by noted quantum computing theorist Scott Aaronson, this book takes readers on a tour through some of the deepest ideas of maths, computer science and physics. Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

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.
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.
Reviews
Pre-Publication Review: "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, MIT, author of Introduction to the Theory of Computation
Pre-Publication Review: "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
Pre-Publication Review: "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 Professor, University of California at Berkeley

本书是关于形式语言、自动机理论和计算复杂性方面的经典教材，是三位理论计算大师的巅峰之作，现已更新到第3版。书中涵盖了有穷自动机、正则表达式与语言、正则语言的性质、上下文无关文法及上下文无关语言、下推自动机、上下文无关语言的，陸质、图灵机、不可判定性以及难解问题等内容。
本书已被世界许多著名大学采用为计算机理论课程的教材或教学参考书，适合用作国内高校计算机专业高年级本科生或研究生的教材，还可供从事理论计算工作的研究人员参考。

This second edition of Grune and Jacobs' brilliant work presents new developments and discoveries that have been made in the field. Parsing, also referred to as syntax analysis, has been and continues to be an essential part of computer science and linguistics. Parsing techniques have grown considerably in importance, both in computer science, ie. advanced compilers often use general CF parsers, and computational linguistics where such parsers are the only option. They are used in a variety of software products including Web browsers, interpreters in computer devices, and data compression programs; and they are used extensively in linguistics.