4 Nov 2013, Published online
16 May 2013, Submitted to a Journal
Uniform Kurtz randomness
(with Takayuki Kihara)
Journal of Logic and Computation, 24 (4): 863-882, 2014
We propose studying uniform Kurtz randomness, which is the uni- form relativization of Kurtz randomness. This notion has more natural properties than the usual relativization. For instance, van Lambalgen’s theorem holds for uniform Kurtz randomness while not for (the usual relativization of) Kurtz randomness. Another advantage is that lowness for uniform Kurtz randomness has many characterizations, such as those via complexity, martingales, Kurtz tt-traceability, and Kurtz dimensional measure.
Oct, 2013. Online
Sep 3, 2011. Accepted
June 7, 2011. Submitted
An optimal superfarthingale and its convergence over a computable topological space
Solomonoff 85th Memorial Conference at Melbourne, Australia.
Lecture Notes in Computer Science
Volume 7070 2013
Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence
Papers from the Ray Solomonoff 85th Memorial Conference, Melbourne, VIC, Australia, November 30 – December 2, 2011
We generalize the convergenece of an optimal semimeasure
to a real probability in algorithmic probability by using game-theoretic
probability theory and the theory of computable topology. Two lemmas
in the proof give as corollary the existence of an optimal test and an
optimal integral test, which are important from the point of view of
algorithmic randomness. We only consider an SCT3 space, where we
can approximate the measure of an open set. Our proof of almost-sure
convergence to the real probability by a superfarthingale indicates why
the convergence in Martin-L¨of sense does not hold.
27 Sep 2013, the slide file was uploaded.
Almost uniform weak n-randomness
Eighth International Conference on Computability, Complexity and Randomness (CCR 2013)
18 Sep 2013, the slide file was uploaded.
Being a Lebesgue point for integral tests
Asian Logic Conference 2013
26 August 2013, the slide file was uploaded.
$L^1$-computability and Schnorr randomness
In a seminar at Universität der Bundeswehr München