Joining non-low C.E. sets with diagonally non-computable functions

Joining non-low C.E. sets with diagonally non-computable functions

We show that every non-low c.e. set joins all Delta sub(2) super(0) diagonally non-computable functions to [empty_set]'. We give two proofs: a direct argument, and a proof using an analysis of functions that are DNC relative to an oracle, extending work by Day and Reimann. The latter proof is a...

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Veröffentlicht in:Journal of logic and computation 2013-12, Vol.23 (6), p.1183-1194
Hauptverfasser: Bienvenu, L., Greenberg, N., Kucera, A., Miller, J. S., Nies, A., Turetsky, D.
Format: Artikel
Sprache:eng
Schlagworte:
Complexity
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Zusammenfassung:We show that every non-low c.e. set joins all Delta sub(2) super(0) diagonally non-computable functions to [empty_set]'. We give two proofs: a direct argument, and a proof using an analysis of functions that are DNC relative to an oracle, extending work by Day and Reimann. The latter proof is also presented in the language of Kolmogorov complexity.
ISSN:0955-792X
1465-363X
DOI:10.1093/logcom/ext039