Results 211 to 220 of about 29,432 (243)

Approximating Kolmogorov complexity

Computability, 2023
It is well known that the Kolmogorov complexity function (the minimal length of a program producing a given string, when an optimal programming language is used) is not computable and, moreover, does not have computable lower bounds. In this paper we investigate a more general question: can this function be approximated?
Ruslan Ishkuvatov, Daniil Musatov, Alexander Shen 0001   +2 more
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On the formalisation of Kolmogorov complexity

Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs, 2021
Kolmogorov complexity is an essential tool in the study of algorithmic information theory, and is used in the fields of Artificial Intelligence, cryptography, and coding theory. The formalisation of the theorems of Kolmogorov complexity is also key to proving results in the theory of Intelligent Agents, specifically the results in Universal Artificial ...
Elliot Catt, Michael Norrish
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Kolmogorov Complexity

2005
Thomas M Cover, Joy A Thomas
exaly   +2 more sources

Kolmogorov-Loveland Stochasticity and Kolmogorov Complexity

Theory of Computing Systems, 2007
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Kolmogorov Complexity and Noncomputability

MLQ, 2002
Summary: We use a method suggested by Kolmogorov complexity to examine some relations between Kolmogorov complexity and noncomputability. In particular we show that the method consistently gives us more information than conventional ways of demonstrating noncomputability (e.g. by embedding in the halting problem).
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Axiomatizing Kolmogorov Complexity

Theory of Computing Systems, 2012
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Kolmogorov Complexity with Error

2006
We introduce the study of Kolmogorov complexity with error. For a metric d, we define Ca(x) to be the length of a shortest program p which prints a string y such that d(x,y) ≤ a. We also study a conditional version of this measure Ca, b(x|y) where the task is, given a string y′ such that d(y,y′) ≤ b, print a string x′ such that d(x,x′) ≤ a.
L. Fortnow (Lance), T. J. Lee (Troy), N.K. Vereshchagin (Nikolay Konstantinovich)   +2 more
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Empirical Kolmogorov Complexity

2018 Information Theory and Applications Workshop (ITA), 2018
The Kolmogorov complexity of a string is the shortest program that outputs that string, and, as such, it provides a deterministic measure of the amount of information within the string that is related, but independent of, Shannon entropy. In practice, this complexity measure is uncomputable and mainly useful for deriving theoretical bounds.
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Entropy and Kolmogorov Complexity

2016
This thesis is dedicated to studying the theory of entropy and its relation to the Kolmogorov complexity. Originating in physics, the notion of entropy was introduced to mathematics by C. E. Shannon as a way of measuring the rate at which information is coming from a data source.
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