News
4 Nov, 2019 The slide file was uploaded.
Title
Reverse randomness
Type
Colloquium talk at Kyoto University on 8 Nov, 2019.
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kyoto
Computable prediction
News
July 2019, Proof reading
Title
Computable prediction
Type
Conference paper
Publication
Miyabe K. (2019) Computable Prediction. In: Hammer P., Agrawal P., Goertzel B., Iklé M. (eds) Artificial General Intelligence. AGI 2019. Lecture Notes in Computer Science, vol 11654. Springer, Cham
DOI https://doi.org/10.1007/978-3-030-27005-6_14
Abstract
We try to predict the next bit from a given finite binary string
when the sequence is sampled from a computable probability measure on the Cantor space.
There exists the best betting strategy among a class of effective ones up to a multiplicative constant,
the induced prediction from which is called algorithmic probability or universal induction by Solomonoff.
The prediction converges to the true induced measure for sufficiently random sequences.
However, the prediction is not computable.
We propose a framework to study the properties of computable predictions.
We prove that all sufficiently general computable predictions also converge to the true induced measure.
The class of sequences along which the prediction converges is related to computable randomness.
We also discuss the speed of the convergence.
We prove that, even when a computable prediction predicts a computable sequence,
the speed of the convergence cannot be bounded by a computable function monotonically decreasing to $0$.
Uniform relativization
News
19 June 2019, Online
Title
Uniform relativization
Type
Conference survey paper
Publication
In: Manea F., Martin B., Paulusma D., Primiero G. (eds) Computing with Foresight and Industry. CiE 2019. Lecture Notes in Computer Science, vol 11558. Springer, Cham
Abstract
This paper is a tutorial on uniform relativization. The usual relativization considers computation using an oracle, and the computation may not work for other oracles, which is similar to Turing reduction. The uniform relativization also considers computation using oracles, however, the computation should work for all oracles, which is similar to truth-table reduction. The distinction between these relativizations is important when we relativize randomness notions in algorithmic randomness, especially Schnorr randomness. For Martin-Löf randomness, its usual relativization and uniform relativization are the same so we do not need to care about this uniform relativization.
We focus on two specific examples of uniform relativization: van Lambalgen’s theorem and lowness. Van Lambalgen’s theorem holds for Schnorr randomness with the uniform relativization, but not with the usual relativization. Schnorr triviality is equivalent to lowness for Schnorr randomness with the uniform relativization, but not with the usual relativization. We also discuss some related known results.
Schnorr triviality via decidable machines
News
29 Mar, 2019 The slide file was uploaded.
Title
Schnorr triviality via decidable machines
Type
Invited talk in CTFM2019
The 9th International Conference on Computability Theory and Foundations of Mathematics
March 21-27, 2019. Wuhan University of Technology, Wuhan, China.
25 Mar, 2019.
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slide
Muchnik degrees and Medvedev degrees of the randomness notions
News
18 Mar, 2019 The slide file was uploaded.
Title
Muchnik degrees and Medvedev degrees of the randomness notions
Type
A talk in AMS
Spring Central and Western Joint Sectional Meeting @ University of Hawaii
Friday March 22, 2019, 3:00 p.m.-4:20 p.m.
Special Session on Computability, Complexity, and Learning, I
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Summary from AMS
Slide