An Introduction to Kolmogorov Complexity and Its Applications

  title={An Introduction to Kolmogorov Complexity and Its Applications},
  author={Ming Li and Paul M. B. Vit{\'a}nyi},
  booktitle={Texts in Computer Science},
Written by two experts in the field, this book is ideal for advanced undergraduate students, graduate students, and researchers in all fields of science. It is self-contained: it contains the basic requirements from mathematics, probability theory, statistics, information theory, and computer science. Included are history, theory, new developments, a wide range of applications, numerous (new) problem sets, comments, source references, and hints to solutions of problems. This is the only… 

Theoretical Computer Science for the Working Category Theorist

In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt Gödel's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more.

Kolmogorov Complexity and Information Content

A central concept in Kolmogorov complexity is revisited in which one would equate program-size complexity with information content, and a number of subtle issues that are at the center of this debate are clarified.

Ker-I Ko and the Study of Resource-Bounded Kolmogorov Complexity

  • E. Allender
  • Computer Science
    Complexity and Approximation
  • 2020
In this brief informal reminiscence, the milieu of the early 1980’s that caused an up-welling of interest in resource-bounded Kolmogorov complexity is reviewed, and some more recent work is discussed that sheds additional light on the questions related to Kolmogoev complexity.

Kolmogorov complexity in the USSR (1975-1982): isolation and its end

These reminiscences are about the "dark ages" of algorithmic information theory in the USSR. After a great interest in this topic in 1960s and the beginning of 1970s the number of people working in

O ct 2 01 9 Non-algorithmic theory of randomness

An alternative language for expressing results of the algorithmic theory of randomness is proposed, more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical results, in principle, applicable in practice.

Theoretical Computer Science: Computational Complexity

An elegant tool for proofs of lower bounds for time/space complexity is a totally different notion of complexity: Kolmogorov complexity which measures the information contents.

Lecture notes on descriptional complexity and randomness

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

Probabilistic Kolmogorov complexity with applications to average-case complexity

A Probabilistic theory of meta-complexity is developed, by incorporating randomness into the notion of complexity of a string x through a new probabilistic variant of time-bounded Kolmogorov complexity that is called pKt complexity.


Using the theory of algorithmic randomness, which is a mix of computability theory and probability theory, the content of some classical theorems is investigated and how this is related to an old question of Kahane and Bollob´as is discussed.

Series Refined Bounds on Kolmogorov Complexity for ω-Languages

Borders on various notions of complexity for ω–languages are investigated by using general Hausdorff measure originally introduced by Felix Hausorf, showing a lower bound for a priori complexity.