Examples of using Kolmogorov complexity in English and their translations into Portuguese
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The set of random strings depends on the choice of the universal Turing machine used to define Kolmogorov complexity, but any choicegives identical asymptotic results because the Kolmogorov complexity of a string is invariant up to an additive constant depending only on the choice of universal Turing machine.
Also, since it can be shown that the Kolmogorov complexity relative to two different universal machines differs by at most a constant,
The set of random strings depends on the choice of the universal Turing machine used to define Kolmogorov complexity, but any choice gives identical asymptotic results because the Kolmogorov complexity of a string is invariant up to an additive constant depending only on the choice of universal Turing machine.
The length of the shortest program that represents the string of bits is called the Kolmogorov complexity.
See also==* Kolmogorov complexity* Incompleteness theorem== References==* Cristian S. Calude 2002.
An example of score function include minimal compression length where a hypothesis with a lowest Kolmogorov complexity has the highest score
Dembski's proposed test is based on the Kolmogorov complexity of a pattern T that is exhibited by an event E that has occurred.
in"An Introduction to Kolmogorov Complexity and Its Applications"(p. 84), write: Ray Solomonoff introduced"Kolmogorov complexity" in a long journal paper in 1964.
Claus-Peter Schnorr proved a characterization in terms of Kolmogorov complexity: a sequence is random if there is a uniform bound on the compressibility of its initial segments.
developed the theory that led to his independent discovery of Kolmogorov complexity.
for some constant"c", for all"n", the Kolmogorov complexity of the initial segment of length"n" of the sequence is at least"n"-"c.
developed the theory that led to his independent discovery of Kolmogorov complexity.
Dembski proposes to view design inference as a statistical test to reject a chance hypothesis P on 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.
BCL has applications in the theory of program-size complexity Kolmogorov complexity.
A far reaching extension of the Gold's approach is developed by Schmidhuber's theory of generalized Kolmogorov complexities, which are kinds of super-recursive algorithms.
Specker sequence J. Schmidhuber,"Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit", International Journal of Foundations of Computer Science, 2002.
The problem of determining the Kolmogorov complexity of a string.
Kolmogorov complexity is not computable.
It can be proven that the Kolmogorov complexity is not computable.
constant terms tend to be disregarded in Kolmogorov complexity theory.