履歴
2025年11月26日：ページ作成
2025年11月23日：受理
2025年7月20日：初稿投稿
タイトル
Randomness with respect to c.e. semimeasures
種類
研究論文
出版情報
Information and Computation
Special Issue in Memory of Vladimir V’yugin
https://doi.org/10.1016/j.ic.2025.105384
要旨
We study algorithmic randomness with respect to c.e. semimeasures, which naturally arise as pushforward measures of partial computable mappings and therefore play a crucial role in algorithmic randomness.
We consider four distinct randomness notions: three based on complexity and one based on tests.
We systematically clarify their inclusion relationships.
Our main contribution is to construct concrete examples that separate these notions.
Furthermore, we investigate how they interact with the classical randomness preservation and no-randomness-from-nothing theorems, identifying precise conditions under which they continue to hold.