Title
Weak L^1-computability and Limit L^1-computability
Type
Talk at
Ninth International Conference on Computability and Complexity in Analysis
June 24-27, 2012, Cambridge, UK
An integral test for Schnorr randomness and its applications
Schnorr triviality is equivalent to being a basis for tt-Schnorr randomness
Title
Schnorr triviality is equivalent to being a basis for tt-Schnorr randomness
Type
Talk at CS seminar in RIMS, Kyoto University on 7 June 2012.
Download
Former half slide in Japanese
The latter half is the same as CCR2012.
Algorithmic interpretation of probability
Title
Algorithmic interpretation of probability
Type
Talk at CAPE lectures, Kyoto University on 29 May 2012.
CAPE lectures
Abstract
Philosophy of probability is one of the big problem in science
discussed so far.
In this talk I first review the history of philosophy of probability.
Then I introduce theory of algorithmic randomness and its
related topic, which is produced by the study of the mathematical
formalization of probability.
Finally I discuss the notion of probability from the algorithmic
point of view by seeing the results that has got recently.
Download
Slide in Japanese
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.
Download
Slide in Japanese