Relations between randomness deficiencies
Logic
2016-08-31 v1
Abstract
The notion of random sequence was introduced by Martin-Loef in 1966. At the same time he defined the so-called randomness deficiency function that shows how close are random sequences to non-random (in some natural sense). Other deficiency functions can be obtained from the Levin-Schnorr theorem, that describes randomness in terms of Kolmogorov complexity. The difference between all of these deficiencies is bounded by a logarithmic term. In this paper we show that the difference between some deficiencies can be as large as possible.
Cite
@article{arxiv.1608.08246,
title = {Relations between randomness deficiencies},
author = {Gleb Novikov},
journal= {arXiv preprint arXiv:1608.08246},
year = {2016}
}