Monthly Archives: February 2012
L^1-computability and weak L^1-computability
Talk at “Kyoto computable analysis Symposium 2012” on 24-27 Feb 2012.
Computable functions are simple functions and
in Weihrauch approach computable functions are always continuous.
However there are some simple discontinuous functions such as the
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.
Schnorr Layerwise Computability
Talk at “Workshop on Proof Theory and Computability Theory 2012” on 20-23 Feb 2012.
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.