Kolmogorov's Contributions to Information Theory and Algorithmic Complexity.

Hershberger Assay was introduced in 1960 to solve this problem.

To link it with the definition given at the beginning, we use the complexity theory of Kolmogorov :

What was later called Kolmogorov Complexity was a side product of his GeneralTheory.

Together with University of Amsterdam Professor Paul Vitanyi, Ming Li pioneered the applications of Kolmogorov complexity.

What was later called Kolmogorov Complexity was a side product of his General Theory.

The Kolmogorov complexity of an object can be viewed as an absolute and objective quantification of the amount of information in it.

Li is playing a key role in developing and demonstrating the power of Kolmogorov complexity, a theory of randomness.

The power of Kolmogorov complexity is that it allows scientists to quantify the randomness of individual objects in an objective and absolute manner.

Kolmogorov complexity is uncomputable: there exists no algorithm that, when input an arbitrary sequence of data, outputs the shortest program that produces the data.

Proving this is a bit tricky, but has been proved using method based on Kolmogorov complexity (e.g. Survey by Vitanyi, page 16).

This condition will naturally impose the fact that checking needs to be in a finite time or in a loop, in short compress the checking, and this is the basis of the complexity theory of Kolmogorov.

While it is true that in a string with low Kolmogorov complexity, there is an underlying rule behind it, it is not true that the "characters or constituents" must "repeat over and over".

For example, the string of length n giving a 1 or 0 depending on whether i is a prime number (for i from 1 to n) has low Kolmogorov complexity, but does not "repeat over and over".