Category: Talks

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The limit of prediction and randomness

Title
The limit of prediction and randomness

Type
Talk at CS seminar in RIMS, Kyoto University on 26 Apr 2012.

Abstract
The former half is about the relation between differentiability and randomness.
I talk about why more computability is needed to characterize Schnorr randomness by differentiability.
The latter half is about the relation between Solomonoff’s induction and the differentiability.
I use a little different setting from Solomonoff’s induction to get a Schnorr randomness version
with long prediction.
I talk more about future work.

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Slide in Japanese

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L^1-computability and weak L^1-computability

Title
L^1-computability and weak L^1-computability

Type
Talk at “Kyoto computable analysis Symposium 2012” on 24-27 Feb 2012.

Abstract
Computable functions are simple functions and
in Weihrauch approach computable functions are always continuous.
However there are some simple discontinuous functions such as the
floor function.
Therefore we need another mathematical notion to measure simplicity.
One candidate is L^1-computability, which was introduced by Pour-El
and Richard 1989.
In this talk I show you that more effectivised version of L^1-computability
has a strong connection with Schnorr randomness
and that some weaker versions of L^1-computability has connections
with some stronger randomness notions.

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slides