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...

kinds of Kolmogorov complexity are studied: the uniform complexity, prefix complexity, monotone complexity, time-bounded Kolmogorov complexity, and space-bounded...

mechanics, algorithmic information theory and computational complexity. Andrey Kolmogorov was born in Tambov, about 500 kilometers southeast of Moscow...

machine used to define Kolmogorov complexity, but any choice gives identical asymptotic results because the Kolmogorov complexity of a string is invariant...

maximal Kolmogorov complexity. The Kolmogorov structure function of an individual data string expresses the relation between the complexity level constraint...

extended Turing test. or by tests which are completely derived from Kolmogorov complexity. Other related tests in this line are presented by Hernandez-Orallo...

that the Kolmogorov complexity is not computable. The proof by contradiction shows that if it were possible to compute the Kolmogorov complexity, then it...

for penalizing complexity in statistical inference. Papers have suggested a connection between Occam's razor and Kolmogorov complexity. One of the problems...

a space of outcomes Ω. Dembski's proposed test is based on the Kolmogorov complexity of a pattern T that is exhibited by an event E that has occurred...

area. The field of Kolmogorov complexity and algorithmic randomness was developed during the 1960s and 1970s by Chaitin, Kolmogorov, Levin, Martin-Löf...

program of small Kolmogorov complexity). The topic has been referenced by other scientific articles. Schmidhuber characterizes low-complexity art as the computer...

algorithmic probability in 1960, publishing the theorem that launched Kolmogorov complexity and algorithmic information theory. He first described these results...

The chain rule[citation needed] for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states: H ( X , Y ) = H ( X...

that is shorter than the string (Chaitin–Kolmogorov randomness); i.e. a string whose Kolmogorov complexity is at least the length of the string. This...

indeed, this result is used to define the concept of randomness in Kolmogorov complexity. It is provably impossible to create an algorithm that can losslessly...

Ingleton's inequality. Kolmogorov complexity satisfies essentially the same inequalities as entropy. Namely, denote the Kolmogorov complexity of a finite string...

probability is closely related to the concept of Kolmogorov complexity. Kolmogorov's introduction of complexity was motivated by information theory and problems...

V(x)=U(h(x))} . An optimal machine is a universal machine that achieves the Kolmogorov complexity invariance bound, i.e. for every machine V, there exists c such...

scientists, Abraham Lempel and Jacob Ziv. This complexity measure is related to Kolmogorov complexity, but the only function it uses is the recursive...

is a Canadian computer scientist, known for his contributions to Kolmogorov complexity, bioinformatics, machine learning theory, and analysis of algorithms...

be deployed in practice. It differs from the related concept of Kolmogorov complexity in that it does not require use of a Turing-complete language to...

correct, for example if sequences of lower Kolmogorov complexity are more probable than sequences of higher complexity, then (as is observed in real life) some...

theory and applications of Kolmogorov complexity. They co-authored the textbook An Introduction to Kolmogorov Complexity and Its Applications, parts...

{some\ c.e.} \ s\mathrm {-gale\ succeeds\ strongly\ on\ } X\}} . Kolmogorov complexity can be thought of as a lower bound on the algorithmic compressibility...

For finite sequences, Kolmogorov defines randomness of a binary string of length n as the entropy (or Kolmogorov complexity) normalized by the length...

the Kolmogorov complexity theory, named for Andrey Kolmogorov. One of the first uses of the incompressibility method with Kolmogorov complexity in the...

Invariance of domain, a theorem in topology A theorem pertaining to Kolmogorov complexity A result in classical mechanics for adiabatic invariants A theorem...

An incompressible string is a string with Kolmogorov complexity equal to its length, so that it has no shorter encodings. The pigeonhole principle can...

ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. The universal prior probability of any prefix p of a computable...

known as algorithmic (Solomonoff–Kolmogorov–Chaitin, Kolmogorov or program-size) complexity together with Andrei Kolmogorov and Ray Solomonoff. Along with...