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Approximating Kolmogorov complexity
Computability, 2023It 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?
Ishkuvatov, Ruslan +2 more
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Axiomatizing Kolmogorov Complexity
Theory of Computing Systems, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Kolmogorov-Loveland Stochasticity and Kolmogorov Complexity
Theory of Computing Systems, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Kolmogorov Complexity and Noncomputability
MLQ, 2002Summary: 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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Empirical Kolmogorov Complexity
2018 Information Theory and Applications Workshop (ITA), 2018The 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
2016This 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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2001
Could the complexity of a thing be measured by a number? Is it necessary for the theory of information to be based on the concepts of theory of probability? Is it possible to partition the set of infinite binary strings into two subsets, namely, the subset of random strings and the other of non-random ones?
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Could the complexity of a thing be measured by a number? Is it necessary for the theory of information to be based on the concepts of theory of probability? Is it possible to partition the set of infinite binary strings into two subsets, namely, the subset of random strings and the other of non-random ones?
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