Is Randomness "Native" to Computer Science?

TL;DR

This paper surveys the development of the concept of randomness in computer science, focusing on Kolmogorov complexity and subsequent formalizations by Martin-Lof, Schnorr, Chaitin, and Levin, highlighting its foundational role.

Contribution

It provides a comprehensive overview of the evolution of the formal notion of randomness in computer science from Kolmogorov's initial ideas to modern theories.

Findings

Kolmogorov's approach links randomness to high information content.

Various formalizations of randomness have been developed over decades.

The survey connects historical and contemporary perspectives on randomness.

Abstract

We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. The original motivation of Kolmogorov was to give up a quantitative definition of information. In this theory, an object is randomness in the sense that it has a large information content. Afterwards, we present parts of the work of Martin-Lof, Schnorr, Chaitin and Levin which supply a mathematical notion of randomness throughout diverse theories from the the 60' up to recently.