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 -
Depth, Highness and DNR degreesArticle

Authors: Philippe Moser 1; Frank Stephan ORCID2

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 1, 2017
Submitted on: November 17, 2015
Keywords: Computer Science - Computational Complexity

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