Category: Publication

News
Mar, 2013, Accepted for the presentation in CiE and rejected to the publication in LNCS
15 Jan, 2013, Submitted to a Conference

Title
Lowness for uniform Kurtz randomness

Type
Accepted in informal electronic proceedings in CiE
with T. Kihara

Journal
Submitted

Abstract
We propose studying uniform Kurtz randomness, which is the uniform relativization of Kurtz randomness. One advantage of this notion is that lowness for uniform Kurtz randomness has many character- izations, such as those via complexity, martingales, Kurtz tt-traceability, and Kurtz dimensional measure.

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preprint

The results in this paper will be appeared in another paper.

News
Dec 25, 2012, Published
Aug 8, 2012, Published online
July 12, 2012, Accepted with a minor revision
Dec 23, 2011, Need to fix it
Oct 18, 2011, Submitted to a Journal

Title
Characterization of Kurtz randomness by a differentiation theorem

Type
Fullpaper

Journal
Theory of Computing Systems: Volume 52, Issue 1 (2013), Page 113-132
The page in TOCS

Abstract
Brattka, Miller and Nies showed that some major algorithmic randomness notions are characterized via differentiability.
The main goal of this paper is to characterize Kurtz randomness by a differentiation theorem on a computable metric space.
The proof shows that characterization by integral tests plays an essential part and shows that how randomness and differentiation are connected.

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The result in this paper was included in L1-computability, layerwise computability and Solovay reducibility

News
Mar 12, 2012, Draft

Title
Weak L^1-computability and Limit L^1-computability

Type
Extended abstract

Journal
in preparation

Abstract
The class of the differences between two integral tests for Schnorr ran- domness is an important class related to Schnorr randomness. In this paper we study other randomness versions. We also claim that Solovay reducibility for lower semicomputable functions generalizes layerwise com- putability.

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in preparation

The result in this paper was included in L1-computability, layerwise computability and Solovay reducibility

News
Jan 26, 2012, Submitted to a conference

Title
An integral test for Schnorr randomness and its application

Type
Fullpaper

Journal
Submitted

Abstract
The author proposed in the previous paper that a characterization of a randomness notion by integral tests is a useful tool to study the relation between algorithmic randomness and computable analysis. In this paper we give a version of Schnorr randomness. With this result we show the connection between L1-computability and Schnorr layerwise computability. Finally we apply them to study the points on which two Radon-Nikodym derivatives are equal.

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