This text offers a comprehensive and accessible treatment of the theory of algorithms and complexity - the elegant body of concepts and methods developed by computer scientists over the past 30 years for studying the performance and limitations of computer algorithms. Among topics covered are: reductions and NP-completeness, cryptography and protocols, randomized algorithms, and approximability of optimization problems, circuit complexity, the "structural" aspects of the P=NP question, parallel computation, the polynomial hierarchy, and many others. Several sophisticated and recent results are presented in a rather simple way, while many more are developed in the form of extensive notes, problems, and hints. The book is surprisingly self-contained, in that it develops all necessary mathematical prerequisites from such diverse fields as computability, logic, number theory, combinatorics and probability.

计算复杂性的现代方法，ISBN：9787510042867，作者：（美）阿罗拉 著

《计算复杂性(英文版)》是理论计算机科学领域的名著。书中对计算任务的固有复杂性研究进行了一般性介绍，涉及了复杂性理论的很多子领域，涵盖了NP完整性、空间复杂性、随机性和计数、伪随机数生成器等内容，还在附录里面给出了现代密码学基础等内容。 《计算复杂性(英文版)》内容严谨，可读性强，适合作为高年级本科生、研究生的教材，对涉及计算复杂性的专业人员也是理想的技术参考书。

本书由计算机理论领域的知名权威Michaael Sipser所撰写。他以独特的视角，系统地介绍了计算机理论的三个主要内容：自动机与语言、可计算性理论和计算复杂性理论。约大部分内容是基本的，同时对可计算性和计算复杂性理论中的某些高级内容进行了重点介绍。作者以清新的笔触、生动的语言给出了宽泛的数学原理，而没有拘泥于某些低层次的细节。在证明之前，均有“证明思路”，帮助读者理解数学形式下涵的概念。同样，对于算法描述，均以直观的文字而非伪代码给出，从而将注意力集中于算法本身，而不是某些模型。新版根据多年来使用本书的教师和学生的建议进行了改进，并对课堂测试题进行了全面的更新，每章末均有样例解答。 本书可作为计算机专业高年级本科生和研究生的教材，也可作为教师和研究人员的参考书。

Assuming only an elementary background in discrete mathematics, this textbook is an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It includes random sampling, expectations, Markov's and Chevyshev's inequalities, Chernoff bounds, balls and bins models, the probabilistic method, Markov chains, MCMC, martingales, entropy, and other topics. The book is designed to accompany a one- or two-semester course for graduate students in computer science and applied mathematics.

本书是计算理论领域的经典著作，被国外多所大学选用为教材。本书以注重思路、深入引导为特色，系统地介绍计算理论的三大主要内容：自动机与语言、可计算性理论和计算复杂性理论。同时，对可计算性和计算复杂性理论中的某些高级内容作了重点讲解。全书通过启发性的问题、精彩的结果和待解决问题来引导读者挑战此领域中的高层次问题。新版的一大亮点是增加了更多习题、教辅资料和部分习题解答，更加有利于教学。 全书叙述由浅入深、详略得当，重点突出，不拘泥于技术细节。可作为计算机专业高年级本科生和研究生的教材，也可作为相关专业教师和研究人员的参考书。

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.