Kolmogorov Complexity: a survey

What follows is a survey of the field of Kolmogorov complexity. Kolmogorov complexity, named after the mathematician Andrej Nikolaevič Kolmogorov, is a measure of the algorithmic complexity of a certain object (represented as a string of symbols) in terms of how hard it is to describe it. This measure dispenses with the need to know the probability distribution that rules a certain object (in general, the distribution may not be defined at all) and is thus more general than Shannon’s entropy, while describing basically the same fact from a slightly different point of view. This paper gives an overview of this field of study from the origins to some of the latest developments and applications.