Muchnik degrees and Medvedev degrees of the randomness notions

News
11 Mar 2018, submitted to a Journal

Title
Muchnik degrees and Medvedev degrees of the randomness notions

Type
Full paper

Journal
TBA

Abstract
The main theme of this paper is computational power when a machine is allowed to access random sets.
The computability depends on the randomness notions and we compare them by Muchnik and Medvedev degrees.
The central question is whether, given an random oracle, one can compute a more random set.
The main result is that, for each Turing functional,
there exists a Schnorr random set whose output is not computably random.

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Muchnikdegrees