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...

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

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...

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

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...

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

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...

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

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...

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

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

such that no specific number can be proved in that system to have Kolmogorov complexity greater than c. While Gödel's theorem is related to the liar paradox...

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

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

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...

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...

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

language) is known as the Kolmogorov complexity of the output, and its mathematical study dates to the work of Andrey Kolmogorov in 1963. Code golf, however...

The speed prior is a complexity measure similar to Kolmogorov complexity, except that it is based on computation speed as well as program length. The...

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

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

Kolmogorov complexity. Together with Leonid A. Levin, he established basic properties of prefix complexity including the formula for the complexity of...