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...

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

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

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

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

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

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

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...

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...

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

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...

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

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...

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

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...

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...

program (that is, a computer program of small Kolmogorov complexity). Schmidhuber characterizes low-complexity art as the computer age equivalent of minimal...

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

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

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

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

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

Algorithmic Randomness and Complexity. Springer. Li, Ming; Vitányi, Paul (1997). An Introduction to Kolmogorov Complexity and Its Applications. Springer...

index of two different partitions of a set. Using the ideas of Kolmogorov complexity, one can consider the mutual information of two sequences independent...

problems in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems...

dependencies (whose source is not an i.i.d. random variable), the Kolmogorov complexity, which quantifies the minimal description length of an object, is...

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...