### Computability of reals on the space where the triangle inequality does not hold

News
2 Sep, 2016, the slide file was uploaded

Title
Computability of reals on the space where the triangle inequality does not hold

Type
Talk at a meeting of Mathematical Society of Japan

slide

### Computability of reals on the space where the triangle inequality does not hold

News
25 July, 2016, the slide file was uploaded

Title
Computability of reals on the space where the triangle inequality does not hold

Type
Talk at a lab seminar

slide

### Variants of layerwise computability

News
6 June 2016, the slide file was uploaded

Title
Variants of layerwise computability

slide(cca2016)

### Randomness and computability

News
3 June 2016, the memo was uploaded

Title
Randomness and computability

Type
Colloquium at Tsukuba University

tsukuba

### Reducibilities relating to Schnorr randomness

News
22 Sep 2014. Accepted to publish in TOCS
24 Mar 2014. Submitted

Title
Reducibilities relating to Schnorr randomness

Type
Full paper

Journal
Theory of Computing Systems, 58(3), 441-462, 2016.
DOI: 10.1007/s00224-014-9583-3

Abstract
Some measures of randomness have been introduced for Martin- L ̈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 (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.