Randomness Conservation Inequalities; Information and Independence in Mathematical Theories

Leonid A. Levin

Randomness Conservation Inequalities; Information and Independence in Mathematical Theories

Computational Complexity 2026-07-26 v1 Information Theory Probability

Authors: Leonid A. Levin

Abstract

The article develops further Kolmogorov's Algorithmic Complexity Theory. The definition of Randomness is modified to satisfy strong invariance properties (conservation inequalities). This allows definitions of concepts such as Mutual Information in individual infinite sequences. Applications to several areas, like Probability Theory, Theory of Algorithms, Intuitionistic Logic are considered. These theories are simplified substantially with the postulate that the objects they consider are independent of (have small mutual information with) any sequence specified by a mathematical property.

Keywords

algorithmic complexity randomness conservation inequalities mutual information independence intuitionistic logic

Cite

@article{arxiv.2607.23830,
  title  = {Randomness Conservation Inequalities; Information and Independence in Mathematical Theories},
  author = {Leonid A. Levin},
  journal= {arXiv preprint arXiv:2607.23830},
  year   = {2026}
}

Comments

15 pages