Monthly Archives: March 2016

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.

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preprint

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Mass problems for randomness notions

News
7 Mar 2016, the slide was uploaded

Title
Mass problems for randomness notions

Type
The mathematical Society of Japan in University of Tsukuba

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slide

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On the notions of randomness and probability

News
6 Mar 2016, the slide was uploaded

Title
On the notions of randomness and probability

Type
A talk in The Third Meeting of Quantum Foundation Club
The slide and the talk is in Japanese.

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slide

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