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• Kolmogorov_complexity abstract "In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov–Chaitin complexity, algorithmic entropy, or program-size complexity) of an object, such as a piece of text, is a measure of the computational resources needed to specify the object. It is named after Andrey Kolmogorov, who first published on the subject in 1963.For example, consider the following two strings of 32 lowercase letters and digits:abababababababababababababababab4c1j5b2p0cv4w1x8rx2y39umgw5q85s7The first string has a short English-language description, namely "ab 16 times", which consists of 11 characters. The second one has no obvious simple description (using the same character set) other than writing down the string itself, which has 32 characters.More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language (the sensitivity of complexity relative to the choice of description language is discussed below). It can be shown that the Kolmogorov complexity of any string cannot be more than a few bytes larger than the length of the string itself. Strings, like the abab example above, whose Kolmogorov complexity is small relative to the string's size are not considered to be complex.The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem.".
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• Kolmogorov_complexity wikiPageWikiLink ASCII.
• Kolmogorov_complexity wikiPageWikiLink Algorithmic_information_theory.
• Kolmogorov_complexity wikiPageWikiLink Algorithmic_probability.
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• Kolmogorov_complexity wikiPageWikiLink Andrey_Kolmogorov.
• Kolmogorov_complexity wikiPageWikiLink Axiomatic_system.
• Kolmogorov_complexity wikiPageWikiLink Bayesian_probability.
• Kolmogorov_complexity wikiPageWikiLink Berry_paradox.
• Kolmogorov_complexity wikiPageWikiLink Berrys_paradox.
• Kolmogorov_complexity wikiPageWikiLink Big-O_notation.
• Kolmogorov_complexity wikiPageWikiLink Big_O_notation.
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• Kolmogorov_complexity wikiPageWikiLink Cantors_diagonal_argument.
• Kolmogorov_complexity wikiPageWikiLink Category:Algorithmic_information_theory.
• Kolmogorov_complexity wikiPageWikiLink Category:Computability_theory.
• Kolmogorov_complexity wikiPageWikiLink Category:Descriptive_complexity.
• Kolmogorov_complexity wikiPageWikiLink Category:Information_theory.
• Kolmogorov_complexity wikiPageWikiLink Category:Measures_of_complexity.
• Kolmogorov_complexity wikiPageWikiLink Chaitins_constant.
• Kolmogorov_complexity wikiPageWikiLink Chris_Wallace_(computer_scientist).
• Kolmogorov_complexity wikiPageWikiLink Combinatorial_proof.
• Kolmogorov_complexity wikiPageWikiLink Complexity.
• Kolmogorov_complexity wikiPageWikiLink Computable_function.
• Kolmogorov_complexity wikiPageWikiLink Computation.
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• Kolmogorov_complexity wikiPageWikiLink Computer_science.
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• Kolmogorov_complexity wikiPageWikiLink Entropy_(information_theory).
• Kolmogorov_complexity wikiPageWikiLink Formal_system.
• Kolmogorov_complexity wikiPageWikiLink Full_employment_theorem.
• Kolmogorov_complexity wikiPageWikiLink Grammar_induction.
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• Kolmogorov_complexity wikiPageWikiLink Gxc3xb6dels_incompleteness_theorem.
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• Kolmogorov_complexity wikiPageWikiLink Incompressible_string.
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• Kolmogorov_complexity wikiPageWikiLink Inductive_inference.
• Kolmogorov_complexity wikiPageWikiLink Inductive_reasoning.
• Kolmogorov_complexity wikiPageWikiLink Interpreter_(computing).
• Kolmogorov_complexity wikiPageWikiLink Java_virtual_machine.
• Kolmogorov_complexity wikiPageWikiLink Juergen_Schmidhuber.
• Kolmogorov_complexity wikiPageWikiLink Jürgen_Schmidhuber.
• Kolmogorov_complexity wikiPageWikiLink Kolmogorov_structure_function.
• Kolmogorov_complexity wikiPageWikiLink Leonid_Levin.
• Kolmogorov_complexity wikiPageWikiLink Levenshtein_distance.
• Kolmogorov_complexity wikiPageWikiLink Lisp_(programming_language).
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• Kolmogorov_complexity wikiPageWikiLink List_of_important_publications_in_theoretical_computer_science.
• Kolmogorov_complexity wikiPageWikiLink Marcus_Hutter.
• Kolmogorov_complexity wikiPageWikiLink Markov_information_source.
• Kolmogorov_complexity wikiPageWikiLink Martingale_(probability_theory).
• Kolmogorov_complexity wikiPageWikiLink Mathematics.
• Kolmogorov_complexity wikiPageWikiLink Matthew_effect.
• Kolmogorov_complexity wikiPageWikiLink Matthew_effect_(sociology).
• Kolmogorov_complexity wikiPageWikiLink Measure_(mathematics).
• Kolmogorov_complexity wikiPageWikiLink Measure_theory.
• Kolmogorov_complexity wikiPageWikiLink Minimum_message_length.
• Kolmogorov_complexity wikiPageWikiLink Multiple_discovery.
• Kolmogorov_complexity wikiPageWikiLink Mutual_information.
• Kolmogorov_complexity wikiPageWikiLink Natural_number.
• Kolmogorov_complexity wikiPageWikiLink Pascal_(programming_language).
• Kolmogorov_complexity wikiPageWikiLink Pigeonhole_principle.
• Kolmogorov_complexity wikiPageWikiLink Probability.
• Kolmogorov_complexity wikiPageWikiLink Proof_by_contradiction.
• Kolmogorov_complexity wikiPageWikiLink Randomness.
• Kolmogorov_complexity wikiPageWikiLink Ray_Solomonoff.
• Kolmogorov_complexity wikiPageWikiLink Self-delimiting_program.
• Kolmogorov_complexity wikiPageWikiLink Self-extracting_archive.
• Kolmogorov_complexity wikiPageWikiLink Solomonoffs_theory_of_inductive_inference.
• Kolmogorov_complexity wikiPageWikiLink String_(computer_science).
• Kolmogorov_complexity wikiPageWikiLink Turing_complete.
• Kolmogorov_complexity wikiPageWikiLink Turing_completeness.
• Kolmogorov_complexity wikiPageWikiLink Turing_degree.
• Kolmogorov_complexity wikiPageWikiLink Turing_machine.
• Kolmogorov_complexity wikiPageWikiLink Uniform_distribution_(discrete).
• Kolmogorov_complexity wikiPageWikiLink Universal_computer.
• Kolmogorov_complexity wikiPageWikiLink Up_to.

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