月: 2012年2月

タイトル
L^1-computability and weak L^1-computability

種類
口頭発表

発表場所
京都計算可能解析学シンポジウム2012
2012年2月24日-27日

アブストラクト
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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タイトル
Schnorr Layerwise Computability

種類
口頭発表

発表場所
証明論及び計算可能性理論に関するワークショップ
“Workshop on Proof Theory and Computability Theory 2012”
2012年2月20日-23日
ワークショップのウェブサイト

アブストラクト
In order to formalize the notion of randomness mathematically,
the theory of algorithmic randomness uses computability theory.
Recent researches show that some notions in algorithmic randomness conversely
are useful to study computable analysis.
One example is layerwise computability defined by Hoyrup and Rojas 2009.
In this talk I introduce Schnorr layerwise computability,
which is a Schnorr-randomness version,
and explain why this is a more natural notion.

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