Philippe Moser ; Frank Stephan - Depth, Highness and DNR degrees

dmtcs:1333 - Discrete Mathematics & Theoretical Computer Science, October 26, 2017, Vol. 19 no. 4, FCT '15 - https://doi.org/10.23638/DMTCS-19-4-2
Depth, Highness and DNR degrees

Authors: Philippe Moser ; Frank Stephan

    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.


    Volume: Vol. 19 no. 4, FCT '15
    Section: special issue FCT'15
    Published on: October 26, 2017
    Accepted on: October 26, 2017
    Submitted on: November 17, 2015
    Keywords: Computer Science - Computational Complexity

    Share

    Consultation statistics

    This page has been seen 444 times.
    This article's PDF has been downloaded 163 times.