Depth, Highness and DNR degrees
Computational Complexity
2023-06-22 v2
Abstract
We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions of O(1)-deepK, O(1)-deepC , order-deep K and order-deep C sequences. Our main results are that Martin-Loef random sets are not order-deepC , that every many-one degree contains a set which is not O(1)-deepC , that O(1)-deepC sets and order-deepK sets have high or DNR Turing degree and that no K-trival set is O(1)-deepK.
Cite
@article{arxiv.1511.05027,
title = {Depth, Highness and DNR degrees},
author = {Philippe Moser and Frank Stephan},
journal= {arXiv preprint arXiv:1511.05027},
year = {2023}
}
Comments
journal version, dmtcs