Sep 2018, accepted
11 Mar 2018, submitted to a Journal
Muchnik degrees and Medvedev degrees of the randomness notions
The joint post-proceedings for ALC2015 and ALC2017 published via World Scientific
Proceedings of the 14th and 15th Asian Logic Conferences, pp. 108-128 (2019) January
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.