An Introduction to Kolmogorov Complexity and Its Applications is popular PDF and ePub book, written by Ming Li in 2013-03-09, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, An Introduction to Kolmogorov Complexity and Its Applications can be Read Online from any device for your convenience.
An Introduction to Kolmogorov Complexity and Its Applications Book PDF Summary
Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Detail Book of An Introduction to Kolmogorov Complexity and Its Applications PDF
- Author : Ming Li
- Release : 09 March 2013
- Publisher : Springer Science & Business Media
- ISBN : 9781475726060
- Genre : Mathematics
- Total Page : 655 pages
- Language : English
- PDF File Size : 16,8 Mb
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