柯尔莫哥洛夫复杂度及其应用导论
An introduction to Kolmogorov complexity and its applications
Ming Li、Paul Vitanyi · 初版 1993 年
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为什么值得读
- 该领域公认的标准教材与必读书目
- 详尽深入讲解条件复杂度等诸多核心理论
- 内容严谨，对信息与复杂度本质提供了深刻见解
本书由该领域的两位专家撰写，非常适合计算机科学、数学、认知科学、哲学、人工智能、统计学和物理学专业的高年级本科生、研究生及研究人员阅读。本书内容自成一体，涵盖了数学和计算机科学的基础要求。书中还包含大量习题集、评注、原始参考文献以及解题提示，并增补了许多第一版中未收录的新内容。
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……Dasgupta-Papadimitriou-Vazirani；Cormen-Leisersen-Rivest-Stein（CLRS《算法导论》）；Kleinberg-Tardos；等等。如果稍微跳出核心 CS 领域，我还很喜欢：- Cover, Thomas 的《信息论基础》（Elements of Information Theory）- 李明、Vitanyi 的《柯尔莫哥洛夫复杂度及其应用导论》（An Introduction to Kolmogorov Complexity and Its Applications）
…Dasgupta-Papadimitriou-Vazirani; Cormen-Leisersen-Rivest-Stein; Kleinberg-Tardos; and more. A bit farther from core CS, I also like: - Cover, Thomas. Elements of Information Theory. - Li, Vitanyi. An Introduction to Kolmogorov Complexity and Its Applications
你手头有更严谨硬核的资料吗？如果想找点“轻松”的睡前读物，可以看看《柯尔莫哥洛夫复杂度及其应用导论》（An Introduction to Kolmogorov Complexity and Its Applications）：http://www.amazon.com/Introduction-Kolmogorov-Complexity-App... 也就是说，热力学定律以极低的柯尔莫哥洛夫复杂度精炼表述了宇宙熵增的过程，这表明……
do you have any resources that are more rigorous? For light bedtime reading, there's An Introduction to Kolmogorov Complexity and Its Applications: http://www.amazon.com/Introduction-Kolmogorov-Complexity-App... That is, the laws of thermodynamics concisely phrase the increasing entropy of the universe with a low Komolgorov complexity, suggesting…
……午餐：你用来把柯尔莫哥洛夫复杂度 K(L, S) 降到 0 的那个技巧，其实增加了 L 本身的复杂度。这是可以被考量进去的，参见“条件柯尔莫哥洛夫复杂度”。李明和维塔尼（Vitányi）合著的《柯尔莫哥洛夫复杂度及其应用导论》（An Introduction to Kolmogorov Complexity and Its Applications）对这点以及更多内容进行了极其详尽的解释，强烈推荐。
…lunch: The trick you use to bring down the Kolgomorov complexity K(L, S) down to 0 increases the complexity of L. This can be taken into account, see "conditional Kolgomorov complexity". The book "An Introduction to Kolmogorov Complexity and Its Applications" by Li and Vitányi explains this, and much more in great detail, and is highly recommended.
标准参考教材是李明和保罗·维塔尼（Paul Vitányi）合著的《柯尔莫哥洛夫复杂度及其应用导论》（An Introduction to Kolmogorov Complexity and Its Applications）。在这个领域它是必读之作。在托马斯·科弗（Thomas Cover）和乔伊·托马斯（Joy Thomas）的《信息论基础》（Elements of Information Theory）里也有一章介绍性内容。这个领域被称为……
The standard reference is "An Introduction to Kolmogorov Complexity and Its Applications", from Ming Li and Paul Vitányi. It is the "must-go" for the subject. An introductory chapter is available in the "Elements of Information Theory" of Thomas Cover and Joy Thomas. The field is called…
感谢分享视频，我会去看的。感兴趣的读者不妨去翻翻李明和维塔尼写的《柯尔莫哥洛夫复杂度及其应用导论》（An Introduction to Kolmogorov Complexity and its Applications，第3版最近刚出）。书价格相对比较贵，不过维塔尼在 CWI 的主页上提供了一些补充资料。
Thanks for the video, I will watch it. The interested readers might want to try the book "An Introduction to Kolmogorov Complexity and its Applications" by Li and Vitanyi (the 3rd edition came out recently). It is comparatively expensive, but Vitanyi's CWI site holds additional material.
Sipser 那本本科计算理论教材[1]里有一章写得极好的入门介绍。如果你想深入探究更硬核的技术细节，那你可能需要看[2]（《柯尔莫哥洛夫复杂度及其应用导论》）。不过这本书相当硬核，胆小脆弱者慎入。[1] http://www.amazon.com/Introduction-Theory-Computation-Michae... [2] http://www.amazon.com/Introduction-Kolmogorov-Complexity-App...
Sipser's undergraduate textbook on the theory of computation[1] has a single, very nice, introductory chapter on the topic. If you want to get technical and deep, you probably want [2] (An introduction to Kolmogorov complexity and its applications). It's pretty hard, though. Not for the faint of heart. [1] http://www.amazon.com/Introduction-Theory-Computation-Michae... [2] http://www.amazon.com/Introduction-Kolmogorov-Complexity-App...