An Introduction to Kolmogorov Complexity and Its Applications

  title={An Introduction to Kolmogorov Complexity and Its Applications},
  author={Ming Li and Paul M. B. Vit{\'a}nyi},
  booktitle={Texts and Monographs in Computer Science},
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 Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and their 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… 
Descriptive Complexity
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  • Computer Science
    Graduate Texts in Computer Science
  • 1999
The core of the book is contained in Chapters 1 through 7, although even here some sections can be omitted according to the taste and interests of the instructor, and the remaining chapters are more independent of each other.
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There are two strings, whose mutual information is large but which have no common information in a strong sense, thus solving the problem posed by Muchnik et al. (1999) and an interpretation of both results in terms of Shannon entropy.
Theory and Applications of Probabilistic Kolmogorov Complexity
An introduction to probabilistic time-bounded Kolmogorov complexity and its applications is provided, highlighting many open problems and research directions.
Kolmogorov Complexity: Sources, Theory and Applications
This special issue contains both material on non-computable aspects of Kolmogorov complexity and material on many fascinating applications based on different ways of approximating Kolmogsorovcomplexity.
Correspondence and Independence of Numerical Evaluations of Algorithmic Information Measures
K_m proves to be a finer-grained measure and a potential alternative approach to lossless compression algorithms for small entities, where compression fails, and a first Beta version of an Online Algorithmic Complexity Calculator (OACC) is announced, based on a combination of theoretical concepts and numerical calculations.
A medley for computational complexity : with applications of information theory, learning theory, and Ketan Mulmuley's parametric complexity technique
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This thesis proves that if a class of functions C has a polynomial-time learning algorithm in Angluin’s bounded error learning model, then if Sat is m-reducible to C, it follows that PH ⊆ P, and that both disjunctive and majority truth-table (non-adaptive) reductions to sparse sets are a special case of m- reductions to linear-threshold functions, and hence the results hold.


An Introduction to Formal Language Theory
This volume intended to serve as a text for upper undergraduate and graduate level students and special emphasis is given to the role of algebraic techniques in formal language theory through a chapter devoted to the fixed point approach to the analysis of context-free languages.
Applications of Kolmogorov Complexity in the Theory of Computation
This exposition gives a brief introduction to the main ideas of Kolmogorov complexity that have been useful in the area of computational complexity theory. We demonstrate how these ideas can actually
The Universal Turing Machine: A Half-Century Survey
This book discusses Alan Turing's analysis of Computability, and major applications of It, and Turing Naturalized: Von Neumann's Unfinished Project.
The Logic in computer science Column
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Mathematical theory of thermodynamics of computation
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Kolmogorov's Early Work on Convergence Theory and Foundation
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Gödel numberings of partial recursive functions
  • H. Rogers
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  • 1958
It will be observed that only concepts that are invariant with respect to general recursive functions are considered; more limited notions of Godel numbering, taking into account, say, primitive recursive structure, are beyond the scope of the present paper.
Generalized Kolmogorov complexity and the structure of feasible computations
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  • Computer Science, Mathematics
    24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
  • 1983
A generalized, two-parameter, Kolmogorov complexity of finite strings is defined which measures how much and how fast a string can be compressed and it is shown that this string complexity measure is an efficient tool for the study of computational complexity.
Lowness Properties of Sets in the Exponential-Time Hierarchy
Ideas from previous studies are incorporated in order to capture the notion of a set being exponentially low in the exponential-time hierarchy.
The Definition of Random Sequences