Reducibilities Relating to Schnorr Randomness

3 years 18 days ago
Reducibilities Relating to Schnorr Randomness
Abstract Some measures of randomness have been introduced for MartinL¨of randomness such as K-reducibility, C-reducibility and vL-reducibility. In this paper we study Schnorr-randomness versions of these reducibilities. In particular, we characterize the computably-traceable reducibility via relative Schnorr randomness, which was asked in Nies’ book [22, Problem 8.4.22]. We also show that Schnorr reducibility implies uniform-Schnorr-randomness version of vL-reducibility, which is the Schnorr-randomness version of the result that K-reducibility implies vL-reducibility. Keywords Algorithmic randomness, Schnorr randomness, van Lambalgen reducibility, Schnorr reducibility, integral test Mathematics Subject Classification (2010) 03D32,68Q30
Kenshi Miyabe
Added 08 Apr 2016
Updated 08 Apr 2016
Type Journal
Year 2016
Where MST
Authors Kenshi Miyabe
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