Depth, Highness and DNR degrees

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...

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Veröffentlicht in:	Discrete mathematics and theoretical computer science Jg. 19 no. 4, FCT '15; H. special issue FCT'15
Hauptverfasser:	Moser, Philippe, Stephan, Frank
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Discrete Mathematics & Theoretical Computer Science 26.10.2017
Schlagworte:	computer science - computational complexity
ISSN:	1365-8050, 1365-8050
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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. Comment: journal version, dmtcs
ISSN:	1365-8050 1365-8050
DOI:	10.23638/DMTCS-19-4-2