An Introduction to Kolmogorov Complexity and Its Applications 3rd Edition by Ming Li (PDF)

Description

The book is outstanding and admirable in many respects. … is necessary reading for all kinds of readers from undergraduate students to top authorities in the field. Journal of Symbolic LogicWritten by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, KolmogorovLoveland randomness, universal learning, communication complexity, Kolmogorov’s random graphs, time-limited universal distribution, Shannon information and others.

User’s Reviews

Editorial Reviews: Review From the reviews of the second edition: “We are indeed in the information age and the scientific exploration of information and the laws that govern its behavior has taken center stage in the dramatic development of sciences. Kolmogorov complexity is a central concept and a powerful tool in the understanding of the quantitative nature of information and its processing and transmission. Li and Vitanyi’s book beautifully captures the elegance of these ideas, their relevance to more of computer science and their theoretical as well as practical applications. The basic concepts of Kolmogorov complexity should be understood by any technically educated person, and they should be studied by all computer scientists. Li and Vitanyi have provided an ideal book for the exploration of a deep, beautiful and important part of the computer science.”Juris Hartmanis, (Turing Award Winner 1993), NSF, Washington D.C.”Special attention is paid to the theory underlying inductive inference and its potential applications. The book is likely to remain the standard treatment of Kolmogorov complexity for a long time.”Jorma J. Rissanen, IBM Research, California”The book of Li and Vitanyi is unexcelled.”Ray J. Solomonoff, Oxbridge Research, Cambridge, Massachusetts”The book is outstanding . . . the authors did their job unbelievably well…necessary reading for all kinds of readers from undergraduate students to top authorities in the field.”Vladimir A. Uspensky and Alexander K. Shen, Journal of Symbolic Logic”It is clear that this book will become ‘the’ Kolmogorov complexity book.”Marius Zimand, Mathematical ReviewsFrom the reviews of the third edition: “Kolmogorov complexity, algorithmic information theory, minimum description length, and other information-based disciplines have experienced a phenomenal explosion in the last decade. … is this third edition worth reading? Yes, it is. The authors have added an extra 204 pages, distributed throughout the book … . Eight new figures were also added. Most impressively, 301 new references were added, bringing the total to 820. … It is sure to maintain its reputation … .” (Jacques Carette, ACM Computing Reviews, April, 2009) From the Back Cover This ongoing bestseller, now in its third edition, is considered the standard reference on Kolmogorov complexity, a modern theory of information that is concerned with information in individual objects.New key features and topics in the 3rd edition:* New results on randomness* Kolmogorov’s structure function, model selection, and MDL* Incompressibility method: counting unlabeled graphs, Shellsort, communication complexity* Derandomization* Kolmogorov complexity versus Shannon information, rate distortion, lossy compression, denoising* Theoretical results on information distance* The similarity metric with applications to genomics, phylogeny, clustering, classification, semantic meaning, question-answer systems*Quantum Kolmogorov complexityWritten by two experts in the field, this book is ideal for advanced undergraduate students, graduate students, and researchers in all fields of science. It is self-contained: it contains the basic requirements from mathematics, probability theory, statistics, information theory, and computer science. Included are history, theory, new developments, a wide range of applications, numerous (new) problem sets, comments, source references, and hints to solutions of problems. This is the only comprehensive treatment of the central ideas of Kolmogorov complexity and their applications.“Li and Vitányi have provided an ideal book for the exploration of a deep, beautiful and important part of computer science.”– Juris Hartmanis, Turing Award Winner 1993, Cornell University, Ithaca, NY.“The book is likely to remain the standard treatment of Kolmogorov complexity for a long time.”– Jorma J. Rissanen, IBM Research, California.“The book of Li and Vitányi is unexcelled.”– Ray J. Solomonoff, Oxbridge Research, Cambridge, Massachusetts”The book is outstanding…the authors did their job unbelievably well…necessary reading for all kinds of readers from undergraduate students to top authorities in the field.”– Vladimir A. Uspensky and Alexander K. Shen, Journal of Symbolic Logic [Review]“Careful and clear introduction to a subtle and deep field.”–David G. Stork, Ricoh Innovations, California, Amazon [Review]“THE book on Kolmogorov Complexity.”–Lance Fortnow, University of Chicago, IL, Amazon [Review]

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A fundamental work in mathematics. I was impressed also by the quality of the shipment, which was made in India with excellent protection of the book which came in France in perfect state. Please thank the sender for his care.

⭐So far this has been a great introduction to the subject. Particularly, I like how much of the prerequisite mathematics and background knowledge is introduced in the “Preliminaries” section. This allows the reader to fill in the gaps she may have in her knowledge, so that she may understand the concepts explored and described throughout the book. It also standardizes the notations throughout, so that readers with different backgrounds and familiar notations can engage with the material. In a sense, for an educated person who is comfortable with quantitative approaches to questions and has some basic understanding of different ideas of mathematics at a undergraduate/advanced high school level, this book is self-contained. It is also thorough, readable, and the study questions at the end of each section provide different challenges for different readers. Overall, I would highly recommend this book to someone interested in various areas such as theory of induction, statistics, the AIXI model of AGI, and general computer science and mathematics.

⭐Le sujet,à savoir la complexité de Kolmogorov, est extrêmement intéressant. Pour le lecteur qui a le temps de lire ce livre en détail, ce qui n’est pas mon cas, il est sans doute possible de tout comprendre sur le sujet. Il y a toutefois trop de définitions à mon gout avant de rentrer dans le vif du sujet même si par endroit, les auteurs proposent divers aperçus historiques très intéressants.E` un libro molto tecnico, ma l’argomento dovrebbe essere insegnato (nelle forme adatte) nelle scuole, e` un fondamentale collegamento tra matematica e filosofia

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