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Kolmogorov complexity

In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is…

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Overview

Definition

Invariance theorem

History and context

Basic results

Compression

Chaitin's incompleteness theorem

Minimum message length

Kolmogorov randomness

Relation to entropy

Halting problem

Time-bounded complexity

Advanced semantic analysis

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Map overview Semantic statistics

Kolmogorov complexity

Nodes82
Edges81
Triples145
Avg. degree1.98
Density0.02439
Components1

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Kolmogorov complexity

Top relations

related to Further reading · 51
Kolmogorov complexity → Algorithmic Randomness, Algoritmusok, An Introduction, Applications, Blum, Brudno, Complexity, Computability, Computation, Control, Course, Cover, CS1, Denis, Downey, Elements, Entropy, Gábor, Hirschfeldt, Information
related to External links · 26
Kolmogorov complexity → Advances, Andrei Nikolaevich KolmogorovChaitin's, Applications, Combinatory Logic Playground, Dowe's Minimum Message Length, Grunwald, Hutter, IDSIA, ISBN, John, John's Lambda Calculus, Kolmogorov Complexity ISBN, Li Vitányi, Minimum Description Length, MIT Press, MML, Myung, Occam's, Pitt, Review
related to history · 12
Kolmogorov complexity → Algorithmic, Control, Formal Theory, General Theory, He, Inductive Inference, Information, Kolmogorov, Part, Preliminary Report, Ray Solomonoff, The
related to Minimum message length · 9
Kolmogorov complexity → Bayesian, Boulton, Cartesian, Dowe, It, Kolmogorov, MML, The, Wallace
related to Kolmogorov randomness · 7
Kolmogorov complexity → Kolmogorov, One, The, There, These, This, To
related to Relation to entropy · 6
Kolmogorov complexity → Brudno, For, It, Kolmogorov, Markov, More
related to Universal probability · 6
Kolmogorov complexity → Define, Fix, In, Kolmogorov, Note, Turing
related to Plain Kolmogorov complexity C · 5
Kolmogorov complexity → By, For, Kolmogorov, The, There
related to Prefix-free Kolmogorov complexity K · 5
Kolmogorov complexity → Equivalently, For, Kolmogorov, The, Turing
related to Chain rule for Kolmogorov complexity · 4
Kolmogorov complexity → It, Kolmogorov, The, Using

Important terminology Word statistics

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Important terminology

complexity length displaystyle kolmogorov program string strings theorem description language universal prefix-free constant information proof textstyle one input leq output

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Kolmogorov complexityis amodified version of Kolmogorov complexity where the space of programs to be searched for a solution is confined to only programs that can run within some pre-defined number of s…0.90text
Kolmogorov complexityrelated to Chain rule for Kolmogorov complexityThe0.60section
Kolmogorov complexityrelated to Chain rule for Kolmogorov complexityKolmogorov0.60section
Kolmogorov complexityrelated to Chain rule for Kolmogorov complexityIt0.60section
Kolmogorov complexityrelated to Chain rule for Kolmogorov complexityUsing0.60section
Kolmogorov complexityrelated to Conditional versionsThe0.60section
Kolmogorov complexityrelated to Conditional versionsKolmogorov0.60section
Kolmogorov complexityrelated to Conditional versionsSo0.60section
Kolmogorov complexityrelated to Conditional versionsThere0.60section
Kolmogorov complexityrelated to External linksThe Legacy0.60section
Kolmogorov complexityrelated to External linksAndrei Nikolaevich KolmogorovChaitin's0.60section
Kolmogorov complexityrelated to External linksIDSIA0.60section

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