classes consisting of models of given maximal Kolmogorov complexity. The Kolmogorov structure function of an individual data string expresses the relation...

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...

described by Kolmogorov's turbulence law Kolmogorov structure function Kolmogorov–Uspenskii machine model Kolmogorov's zero–one law Kolmogorov–Zurbenko filter...

after Andrey Kolmogorov and Nikolai Smirnov. The Kolmogorov–Smirnov statistic quantifies a distance between the empirical distribution function of the sample...

mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair of distinct points of X, at least...

statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there...

approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function f : [ 0 , 1 ] n...

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

In mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, is an explanation of the meaning of proof in intuitionistic...

mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited...

Rissanen bases the mathematical underpinning of MDL on the Kolmogorov structure function. According to the MDL philosophy, Bayesian methods should be...

mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem)...

the "Kolmogorov −⁠5/3⁠ spectrum" is generally observed in turbulence. However, for high order structure functions, the difference with the Kolmogorov scaling...

distributions going back to the 1920s. In a 1932 paper, Kolmogorov derived a characteristic function for random variables associated with Lévy processes....

{F}}_{n}-F\|_{\infty }>z{\Big )}\leq 2e^{-2z^{2}}.} In fact, Kolmogorov has shown that if the cumulative distribution function F is continuous, then the expression n ‖ F...

structures; continuous functions, which preserve topological structures; and differentiable functions, which preserve differential structures. In 1939, the French...

estimates depending on the regularity of the target function and of the activation function. The Kolmogorov–Arnold representation theorem is similar in spirit...

Knuth–Morris–Pratt algorithm Königsberg bridges problem Kolmogorov complexity Kraft's inequality Kripke structure Kruskal's algorithm kth order Fibonacci numbers...

as λ-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped...

regular spaces and Tychonoff spaces are related through the notion of Kolmogorov equivalence. A topological space is Tychonoff if and only if it's both...

between algebraic structures is a function that is compatible with the operations of the structures. For all common algebraic structures, and, in particular...

theory; see interpretation (model theory). In database theory, structures with no functions are studied as models for relational databases, in the form of...

important). This is the way how σ-algebras arise in (Kolmogorov's) probability theory, where real-valued functions on the sample space Ω are real-valued random...

possible functions (in the set-theoretic sense of "function") are Kolmogorov random, and hence the NFL theorems apply to a set of functions almost all...

Martin-Löf received his PhD in 1970 from Stockholm University, under Andrey Kolmogorov. Martin-Löf is an enthusiastic bird-watcher; his first scientific publication...

result is equivalent to a Fourier transform of Kolmogorov's 1941 result for the turbulent structure function. The pressure fluctuations in a turbulent flow...

characteristic function of a subset of the natural numbers) is random or not by invoking a notion of randomness for finite objects. Kolmogorov complexity...

Recursive Functions". Journal of the ACM. 14 (2): 322–336. doi:10.1145/321386.321395. S2CID 15710280. Burgin, M. (1982). "Generalized Kolmogorov complexity...

regression models propose that Y i {\displaystyle Y_{i}} is a function (regression function) of X i {\displaystyle X_{i}} and β {\displaystyle \beta } ...

In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all...