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...

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

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

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...

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

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

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

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

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

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

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

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...

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

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

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

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...

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...

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

linear complexity, provide spectral measures of randomness. T. Beth and Z-D. Dai purported to show that Kolmogorov complexity and linear complexity are practically...

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

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

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...

humans perceive relevance, cognitive complexity is defined as an extension of the notion of Kolmogorov complexity. It amounts to the length of the shortest...

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...

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

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

Kolmogorov complexity is mildly hard on average. Since the existence of one-way functions implies that polynomial-time bounded Kolmogorov complexity is...

good solution. Almost all objective functions are of such high Kolmogorov complexity that they cannot be stored in a particular computer. More precisely...