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Kolmogorov Complexity and Chaotic Phenomena
 International Journal of Engineering Science
, 2002
"... Born about three decades ago, Kolmogorov Complexity Theory (KC) led to important discoveries that, in particular, give a new understanding of the fundamental problem: interrelations between classical continuum mathematics and reality (physics, biology, engineering sciences, . . . ). ..."
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Cited by 8 (7 self)
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Born about three decades ago, Kolmogorov Complexity Theory (KC) led to important discoveries that, in particular, give a new understanding of the fundamental problem: interrelations between classical continuum mathematics and reality (physics, biology, engineering sciences, . . . ).
Shannon Information and Kolmogorov Complexity
, 2010
"... The elementary theories of Shannon information and Kolmogorov complexity are cmpared, the extent to which they have a common purpose, and where they are fundamentally different. The focus is on: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual in ..."
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Cited by 2 (1 self)
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The elementary theories of Shannon information and Kolmogorov complexity are cmpared, the extent to which they have a common purpose, and where they are fundamentally different. The focus is on: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual
Topological arguments for Kolmogorov complexity ∗
"... We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties. 1 ..."
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Cited by 2 (1 self)
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We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties. 1
Kolmogorov complexity and derandomization
, 2004
"... Kolmogorov complexity is a measure that describes the compressibility of a string. Strings with low complexity contain a lot of redundancy, while strings with high Kolmogorov complexity seem to lack any kind of pattern. For instance, a string such as 5555 5555 5555 5555 5555 has low complexity, whil ..."
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Kolmogorov complexity is a measure that describes the compressibility of a string. Strings with low complexity contain a lot of redundancy, while strings with high Kolmogorov complexity seem to lack any kind of pattern. For instance, a string such as 5555 5555 5555 5555 5555 has low complexity
Quit Kolmogorov Complexity
"... • The best way to describe the complexity of a given string s is to find its Kolmogorov complexity K(s). • K(s) is the shortest length of a program that computes s. • For example, a sequence is random if and only if its Kolmogorov complexity is close to its length. • We can check how close are two D ..."
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• The best way to describe the complexity of a given string s is to find its Kolmogorov complexity K(s). • K(s) is the shortest length of a program that computes s. • For example, a sequence is random if and only if its Kolmogorov complexity is close to its length. • We can check how close are two
Inequalities for Shannon entropies and Kolmogorov complexities
, 1997
"... The paper investigates connections between linear inequalities that are valid for Shannon entropies and for Kolmogorov complexities. ..."
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Cited by 39 (9 self)
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The paper investigates connections between linear inequalities that are valid for Shannon entropies and for Kolmogorov complexities.
MUSIC ANALYSIS AND KOLMOGOROV COMPLEXITY
"... The goal of music analysis is to find the most satisfying explanations for musical works. It is proposed that this can best be achieved by attempting to write computer programs that are as short as possible and that generate representations that are as detailed as possible of the music to be explain ..."
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Cited by 1 (1 self)
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to be explained. The theory of Kolmogorov complexity suggests that the length of such a program can be used as a measure of the complexity of the analysis that it represents. The analyst therefore needs a way to measure the length of a program so that this length reflects the quality of the analysis
KOLMOGOROV COMPLEXITY AND SOLOVAY FUNCTIONS
, 2009
"... Solovay [19] proved that there exists a computable upper bound f of the prefixfree Kolmogorov complexity function K such that f(x) = K(x) for infinitely many x. In this paper, we consider the class of computable functions f such that K(x) ≤ f(x)+O(1) for all x and f(x) ≤ K(x) + O(1) for infinit ..."
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Cited by 14 (6 self)
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Solovay [19] proved that there exists a computable upper bound f of the prefixfree Kolmogorov complexity function K such that f(x) = K(x) for infinitely many x. In this paper, we consider the class of computable functions f such that K(x) ≤ f(x)+O(1) for all x and f(x) ≤ K(x) + O(1
1Kolmogorov Complexity
"... Information theory is a branch of mathematics that attempts to quantify information. To quantify information one needs to look at the data compression and transmission rate. Information theory has applications in many fields. The purpose of this paper is comprehensively present a subset of informati ..."
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of information theory as it applies to computer science. Andrei Kolmogorov was the pioneering mathematician that applied information theory to computer science. The branch of information theory that relates to computer science became known as Kolmogorov complexity or algorithmic complexity. I.
On the Application of Kolmogorov Complexity to
"... This paper presents a proposal for the application of Kolmogorov complexity to the characterization of systems and processes, and the evaluation of computational models. The methodology developed represents a theoretical tool to solve problems from systems science. Two applications of the methodolog ..."
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This paper presents a proposal for the application of Kolmogorov complexity to the characterization of systems and processes, and the evaluation of computational models. The methodology developed represents a theoretical tool to solve problems from systems science. Two applications
Results 11  20
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980