Lecture notes on descriptional complexity and randomness

TL;DR

This paper provides a concise survey of the foundational concepts and techniques in Algorithmic Information Theory, focusing on descriptional complexity and randomness, suitable for educational purposes.

Contribution

It offers a didactical overview of key ideas and methods in Algorithmic Information Theory, emphasizing clarity over extensive background.

Findings

Introduces core concepts of descriptional complexity and randomness

Summarizes main techniques used in Algorithmic Information Theory

Provides an evolving, accessible presentation for learners

Abstract

A didactical survey of the foundations of Algorithmic Information Theory. These notes are short on motivation, history and background but introduce some of the main techniques and concepts of the field. The "manuscript" has been evolving over the years. Please, look at "Version history" below to see what has changed when.