$$\textit{K}$$ -trivial, $$\textit{K}$$ -low and $${{\mathrm{\textit{MLR}}}}$$ -low Sequences: A Tutorial

A constructive version of Birkhoffʼs ergodic theorem for Martin-Löf random points

Algorithmic Information Theory and Foundations of Probability

Algorithmic Statistics Revisited

Algorithmic Statistics: Forty Years Later

article published in 2016

Algorithmic tests and randomness with respect to a class of measures

article

Algorithms and Geometric Constructions

scholarly article by Vladimir Uspenskiy & Alexander Shen published 2018 in Lecture Notes in Computer Science

An Additivity Theorem for Plain Kolmogorov Complexity

Around Kolmogorov Complexity: Basic Notions and Results

article

Combinatorial interpretation of Kolmogorov complexity

Complex tilings

Conditional Probabilities and van Lambalgen’s Theorem Revisited

Descriptive complexity of computable sequences

Dimension 1 sequences are close to randoms

Effective Closed Subshifts in 1D Can Be Implemented in 2D

Ergodic-Type Characterizations of Algorithmic Randomness

Fixed Point and Aperiodic Tilings

Fixed-point tile sets and their applications

Game Arguments in Computability Theory and Algorithmic Information Theory

Generic algorithms for halting problem and optimal machines revisited ⬇️

High Complexity Tilings with Sparse Errors

Hilbert’s Error?

scholarly article by Alexander Shen published 18 September 2018 in The Mathematical Intelligencer

IP = SPACE: simplified proof

Inequalities for Shannon Entropy and Kolmogorov Complexity

Insuring against loss of evidence in game-theoretic probability

article

Kolmogorov Complexity as a Language

Layerwise Computability and Image Randomness

Letters to the editor

scientific article (publication date: September 2001)

Limit Complexities Revisited

Logical operations and Kolmogorov complexity

article

Mathematical entertainments

Article from The Mathematical Intelligencer

Non-reducible Descriptions for Conditional Kolmogorov Complexity

Non-reducible descriptions for conditional Kolmogorov complexity

Nonsense

a scholarly article

Not every domain of a plain decompressor contains the domain of a prefix-free one

On-Line Probability, Complexity and Randomness

Opinion

scholarly article (1994)

Partitioning multi-dimensional sets in a small number of “uniform” parts

Prequential Randomness

Prequential randomness and probability

Random Semicomputable Reals Revisited

SETS OF K-INDEPENDENT STRINGS

Test Martingales, Bayes Factors and p -Values

The Arrest of Victor Vassiliev

The Kučera–Gács theorem revisited by Levin

scientific article published in 2023

The axiomatic power of Kolmogorov complexity

Topological Arguments for Kolmogorov Complexity

Upper semi-lattice of binary strings with the relation “x is simple conditional to y”

Variations on Muchnik’s Conditional Complexity Theorem

Variations on Muchnik’s Conditional Complexity Theorem

What Percentage of Programs Halt?

article published in 2015