Title
Characterizing randomness by integral tests
Type
Talk
This talk is in CS Seminar at Kyoto University on June 16, 2011.
The same talk will be given in CiE 2011.
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宮部賢志(ミヤベケンシ)
Title
Characterizing randomness by integral tests
Type
Talk
This talk is in CS Seminar at Kyoto University on June 16, 2011.
The same talk will be given in CiE 2011.
Download
slide
The content of the paper will be merged into Algorithmic randomness over general spaces.
News
June 13, 2011, Rejected
Sep 21, 2010, Submitted to a Journal
Title
A computable topological space of measures
Type
Fullpaper
Journal
submitted
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Japanese summary
Abstract
We show that the space of bounded non-negative Borel measures on
a computable topological space is also a computable topological space
with A-topology. Then we dene computable measures which may not
be probabilistic and may be even innite. We also study randomness for
non-negative Borel measures which may not be probabilistic.
News
Mar 19, 2011. Added citation information
Mar 7, 2011. Published online
May 18, 2010. The paper “Truth-table Schnorr randomness and truth-table reducible randomness” is accepted by Mathematical Logic Quarterly on May 18, 2010.
Title
Truth-table Schnorr randomness and truth-table reducible randomness
Type
Fullpaper
Journal
Mathematical Logic Quarterly 57(3):323-338, 2011
DOI 10.1002/malq.200910128
Journal Page
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preprint
Japanese summary
Abstract
Schnorr randomness and computably randomness are natural concepts of random sequences. However van Lambalgen’s Theorem fails for both randomnesses. In this paper we define truth-table Schnorr randomness (defined by Franklin and Stephan too only by martingales) and truth-table reducible randomness, for which we prove that van Lambalgen’s Theorem holds. We also show that the classes of truth-table Schnorr random reals relative to a high set contain reals Turing equivalent to the high set. It follows that each high Schnorr random real is half of a real for which van Lambalgen’s Theorem fails. Moreover we establish the coincidence between triviality and lowness notions for truth-table Schnorr randomness.
Cited by
@article{franklin2009van,
title={{van Lambalgen’s Theorem and high degrees}},
author={Franklin, J.N.Y. and Stephan, F.},
year={2009},
publisher={Submitted}
}
@misc{bienvenucharacterizing,
title={Characterizing lowness for Demuth randomness},
author={Bienvenu, L. and Downey, R. and Greenberg, N. and Nies, A. and Turetsky, D.},
publisher={Submitted}
}
News
Feb, 2011, Published
Dec 13, 2010, Submitted
Title
Generalizing randomness
Type
Survey
Journal
RIMS Kokyuroku
No. 1729
“Formal Systems and Computability Theory” (2010/09/13-2010/09-17)
pp. 84-94
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preprint
Title
Computability of measures and A-topology
Type
Talk
This talk is in “CC-Seminar” at Kyoto Sangyo University on Mar 4, 2011.
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slide
Attached slides are in English.