Kolmogorov complexity

Kolmogorov complexity depends on what computer language is used.

Strings whose Kolmogorov complexity is small relative to the string's size are not considered to be complex.

For that reason, constant terms tend to be disregarded in Kolmogorov complexity theory.

From the standpoint of Kolmogorov complexity theory, this calculation is problematic.

The problem of determining the Kolmogorov complexity of a string.

It can be proven that the Kolmogorov complexity is not computable.

Others have employed Kolmogorov complexity to show that God is complex.

To define the Kolmogorov complexity, we must first specify a description language for strings.

There are several other variants of Kolmogorov complexity or algorithmic information.

Some strings are incompressible by any algorithm - see Kolmogorov complexity.

Algorithmic probability is closely related to the concept of Kolmogorov complexity.

The mathematics of Kolmogorov complexity describes the challenges and limits of this.

Unfortunately, there is no general solution because Kolmogorov complexity is not computable.

Moreover, to express the length of one uses the notion of Kolmogorov complexity.

In practice, almost all objective functions and algorithms are of such high Kolmogorov complexity that they cannot arise.

The axiomatic approach encompasses other approaches to Kolmogorov complexity.

In theoretical computer science this field of study is known as Kolmogorov complexity, or the smallest program which outputs a given string.

They effectively have a different Kolmogorov complexity.

Consider model classes consisting of models of given maximal Kolmogorov complexity.

Kolmogorov complexity became not only a subject of independent study but is also applied to other subjects as a tool for obtaining proofs.

His original definition involved measure theory, but it was later shown that it can be expressed in terms of Kolmogorov complexity.

Recent papers have suggested a connection between Occam's razor and Kolmogorov complexity.

The equivalent statement for Kolmogorov complexity does not hold exactly; it is true only up to a logarithmic term:

Dai showed that Kolmogorov complexity and linear complexity are practically the same.

Fundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity.