The way to capture the notion of probability

News
24 Apr. 2013, the slides were uploaded.

Title
The way to capture the notion of probability

Type
Talk at seminar of Hasuo group

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slide

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The other history of probability theory

News
19 Mar 2013, the manuscript and the slides were uploaded.

Title
The other history of probability theory

Type
Mathematical Society of Japan
20-21 Mar 2013, Kyoto University

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予稿
スライド

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Van Lambalgen’s Theorem for uniform Kurtz randomness

News
19 Mar 2013, the manuscript and the slides were uploaded.

Title
Van Lambalgen’s Theorem for uniform Kurtz randomness

Type
Mathematical Society of Japan
20-21 Mar 2013, Kyoto University

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preliminary report
slides

Correction
The preliminary report contains an error. I pointed it out in the slides.

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Computation with advice of degree of randomness

News
15 Mar 2013, Submitted

Title
Computation with advice of degree of randomness

Type
Survey

Journal
RIMS Kokyuroku
28 – 30 Jan 2013

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preprint

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Analytical approach to algorithmic randomness

News
30 Nov 2012, Submitted

Title
Analytical approach to algorithmic randomness

Type
Survey

Journal
RIMS Kokyuroku
PROOF THEORY AND COMPLEXITY 2012
12 -14 Sep 2012

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preprint

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Schnorr and Kurtz randomness versions of Merkle’s criterion

News
19 Mar 2013, the manuscript and the slides were uploaded.

Title
Schnorr and Kurtz randomness versions of Merkle’s criterion

Type
COMP
Gifu University, 18 Mar 2013
IEICE Technical Report Vol. 112 No. 498, COMP 2012-60, pp55-59

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slides (in Japanese)
preprint (in Japanese)

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Things to do in and with algorithmic randomness

News
23 Feb 2013, the slides were uploaded.

Title
Things to do in and with algorithmic randomness

Type
Talk
Sendai Logic School 2013
http://sendailogic.math.tohoku.ac.jp/SLS/
Sendai, 22 Feb 2013

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Slide

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Computably measurable sets and computably measurable functions in terms of algorithmic randomness

News
20 Feb 2013, the slides were uploaded.

Title
Computably measurable sets and computably measurable functions in terms of algorithmic randomness

Type
Talk
Computability Theory and Foundations of Mathematics
http://sendailogic.math.tohoku.ac.jp/CTFM/
Tokyo Tech, 20 Feb 2013

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slide

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Van Lambalgen’s Theorem for uniformly relative Schnorr and computable randomness

News
Feb 2013, accepted
26 Sep 2012, uploaded to arXiv
Aug 2012, submitted

Title
Van Lambalgen’s Theorem for uniformly relative Schnorr and computable randomness
(with Jason Rute)

Type
Full paper

Journal
Proceedings of the Twelfth Asian Logic Conference, World Scientific, 251-270

Abstract
We correct Miyabe’s proof of van Lambalgen’s Theorem for truth-table Schnorr randomness (which we will call uniformly rela- tive Schnorr randomness). An immediate corollary is one direction of van Lambalgen’s theorem for Schnorr randomness. It has been claimed in the literature that this corollary (and the analogous result for com- putable randomness) is a “straightforward modification of the proof of van Lambalgen’s Theorem.” This is not so, and we point out why. We also point out an error in Miyabe’s proof of van Lambalgen’s Theorem for truth-table reducible randomness (which we will call uniformly rel- ative computable randomness). While we do not fix the error, we do prove a weaker version of van Lambalgen’s Theorem where each half is computably random uniformly relative to the other.

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Download from arXiv

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Computability of conditional probability

News
26 Jan 2013, the slides were uploaded.

Title
Computability of conditional probability

Type
Talk
LA symposium, Kyoto University, 28 Jan 2013

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preliminary report
slide

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