Propagation of partial randomness
Logic
2013-11-05 v1
Abstract
Let f be a computable function from finite sequences of 0's and 1's to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-L"of random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f-randomness relative to a PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree.
Keywords
Cite
@article{arxiv.1311.0724,
title = {Propagation of partial randomness},
author = {Kojiro Higuchi and W. M. Phillip Hudelson and Stephen G. Simpson and Keita Yokoyama},
journal= {arXiv preprint arXiv:1311.0724},
year = {2013}
}
Comments
27 pages. A version of this paper will appear in Annals of Pure and Applied Logic