宮部賢志（ミヤベケンシ）
履歴
2013年3月 CiEにて発表受理，LNCSには非採択
2013年1月15日 投稿
タイトル
Lowness for uniform Kurtz randomness
種類
会議
T. Kiharaとの共著
雑誌
Sumitted
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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プレプリント
この論文の結果は他の結果と一緒に別の論文に含める予定です．
履歴
2012年12月25日出版
2012年8月8日オンライン
2012年7月12日アクセプト報告
2011年10月18日投稿
タイトル
Characterization of Kurtz randomness by a differentiation theorem
種類
論文
雑誌
Theory of Computing Systems: Volume 52, Issue 1 (2013), Page 113-132
TOCSでのページ
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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プレプリント
本論文の結果はL1-computability, layerwise computability and Solovay reducibilityに含めることになりました．
履歴
2012年3月12日ドラフト
タイトル
Weak L^1-computability and Limit L^1-computability
種類
拡大版要旨
国際会議と雑誌
準備中
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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準備中
本論文の結果はL1-computability, layerwise computability and Solovay reducibilityに含めることになりました．
履歴
2012年1月26日投稿
タイトル
An integral test for Schnorr randomness and its application
種類
論文
国際会議と雑誌
投稿中
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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preprint