Randomness
Algorithmic randomness
- Effective aspects of algorithmically random structures
- Randomness and Mathematical Proof
- Muchnik and Medvedev degrees of randomness
- Algorithmic Randomness as Foundation of Inductive Reasoning and AI
- Algorithmic Randomness and Probabilistic Laws
- The mathematical foundations of randomness (introductory)
- Algorithmically random series
- Kolmogorov complexity as a combinatorial tool
- Continuous randomness via transformations of 2-random sequences
- Solovay reducibility via translation functions on rationals and on reals
- Variants of Solovay reducibility
Van Lambalgen’s theorem
Van Lambalgen’s theorem relates randomness in two dimensions with randomness in one dimension.
LR degrees
- Almost everywhere domination and superhighness
- Almost Everywhere Domination
- Mass Problems and Almost Everywhere Domination
Diophantine approximation and randomness
Diophantine approximation is a way to measure hardness of approximations.
- Irrationality Exponent, Hausdorff Dimension and Effectivization
- On the construction of absolutely normal numbers
- The irrationality exponents of computable numbers
- On simply normal numbers to different bases
- A polynomial-time algorithm for computing absolutely normal numbers
- On the normality of numbers in different bases
- Normal numbers and the Borel hierarchy
- A computable absolutely normal Liouville number. Mathematics of Computation