Layerwise computability and image randomness
Logic
2016-07-15 v1 Information Theory
math.IT
Probability
Abstract
Algorithmic randomness theory starts with a notion of an individual random object. To be reasonable, this notion should have some natural properties; in particular, an object should be random with respect to image distribution if and only if it has a random preimage. This result (for computable distributions and mappings, and Martin-L\"of randomness) was known for a long time (folklore); in this paper we prove its natural generalization for layerwise computable mappings, and discuss the related quantitative results.
Cite
@article{arxiv.1607.04232,
title = {Layerwise computability and image randomness},
author = {Laurent Bienvenu and Mathieu Hoyrup and Alexander Shen},
journal= {arXiv preprint arXiv:1607.04232},
year = {2016}
}