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    Depth, Highness and DNR degrees

    Moser, Philippe and Stephan, Frank (2017) Depth, Highness and DNR degrees. Discrete Mathematics and Theoretical Computer Science, 19 (4). p. 2. ISSN 1462-7264

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    We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions ofO(1)-deepK,O(1)-deepC, order-deepKand order-deepCsequences. Our main results are that Martin-L ̈of randomsets are not order-deepC, that every many-one degree contains a set which is notO(1)-deepC, thatO(1)-deepCsetsand order-deepKsets have high or DNR Turing degree and that noK-trival set isO(1)-deepK.

    Item Type: Article
    Keywords: Bennett logical depth; Kolmogorov complexity; algorithmic randomness theory; computability and ran-domness;
    Academic Unit: Faculty of Science and Engineering > Computer Science
    Item ID: 11674
    Identification Number:
    Depositing User: Philippe Moser
    Date Deposited: 12 Nov 2019 12:45
    Journal or Publication Title: Discrete Mathematics and Theoretical Computer Science
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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