履歴
2017年2月1日 TOCS受理
タイトル
Coherence of reducibilities with randomness notions
種類
正論文
国際会議と雑誌
Theory of Computing Systems – October 2018, Volume 62, Issue 7, pp 1599–1619
DOI: https://doi.org/10.1007/s00224-017-9752-2
Abstract
Loosely speaking, when $A$ is “more random” than $B$ and $B$ is “random”,
then $A$ should be random.
The theory of algorithmic randomness has some formulations of “random” sets
and “more random” sets.
In this paper, we study which pairs $(R,r)$ of randomness notions $R$
and reducibilities $r$ have the follwing property:
if $A$ is $r$-reducible to $B$ and $A$ is $R$-random,
then $B$ should be $R$-random.
The answer depends on the notions $R$ and $r$.
The implications hold for most pairs, but not for some.
We also give characterizations of $n$-randomness via complexity.
ダウンロード
preprint