# An Introduction to Kolmogorov Complexity and Its Applications

@inproceedings{Li1993AnIT, 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}, year={1993} }

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…

## 3,866 Citations

Descriptive Complexity

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- 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.

Kolmogorov Complexity: Recent Research in Moscow

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The goal of this talk is to state some of the questions and the results obtained in Moscow during the last years of Kolmogorov complexity theory.

Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines

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A novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings, which promises to deliver a range of applications, and to provide insight into the question of complexity calculation of finite (and short) strings.

Around Kolmogorov complexity: basic notions and results

- Computer ScienceArXiv
- 2015

This chapter attempts to fill the gap in the basic notions of algorithmic information theory and covers the basic properties of Kolmogorov complexity, Solomonoff universal a priori probability, notions of randomness, and effective Hausdorff dimension.

Dynamics, measure and dimension in the theory of computing

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- 2009

This thesis establishes some results in algorithmic information theory. Martin-Lof in 1966 formalized the notion of what it means for a given sequence to be random, using the theory of computation.…

Logical operations and Kolmogorov complexity. II

- Computer Science, MathematicsProceedings 16th Annual IEEE Conference on Computational Complexity
- 2001

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

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2022

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

- Computer ScienceComput. J.
- 1999

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

- Computer ScienceComput.
- 2013

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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- 2014

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.

## References

SHOWING 1-10 OF 373 REFERENCES

An Introduction to Formal Language Theory

- Computer ScienceTexts and Monographs in Computer Science
- 1988

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

- Computer Science
- 1990

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

- Computer Science
- 1992

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

- MathematicsBull. EATCS
- 1989

It is shown that, if the authors restrict thesauri by requiring their probability distributions to be uniform, then they and parametric conditions are equivalent, and the thesaurus point of view suggests some possible extensions of the theory.

Mathematical theory of thermodynamics of computation

- Computer Science
- 1992

The fundamental theorem connects physics to mathematics, providing the key that makes such a theory possible, and establishes optimal upper and lower bounds on the ultimate thermodynamic cost of computation.

Kolmogorov's Early Work on Convergence Theory and Foundation

- Mathematics
- 1989

1. Probability before Kolmogorov. When Kolmogorov was starting his mathematical career, nonmathematical probability was, as it still is, the study of various not very precisely defined real contexts.…

Gödel numberings of partial recursive functions

- MathematicsJournal of Symbolic Logic
- 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

- Computer Science, Mathematics24th 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

- Computer Science, MathematicsSIAM J. Comput.
- 1988

Ideas from previous studies are incorporated in order to capture the notion of a set being exponentially low in the exponential-time hierarchy.