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

• Type: Journal
• Year: 2016
• Where: MST
• Authors: Kenshi Miyabe
• Keywords: Hardware, MST 2016