When does randomness come from randomness?
Theor. Comput. Sci.(2016)
摘要
A result of Shen says that if F : 2 N ź 2 N is an almost-everywhere computable, measure-preserving transformation, and y ź 2 N is Martin-Löf random, then there is a Martin-Löf random x ź 2 N such that F ( x ) = y . Answering a question of Bienvenu and Porter, we show that this property holds for computable randomness, but not Schnorr randomness. These results, combined with other known results, imply that the set of Martin-Löf randoms is the largest subset of 2 N satisfying this property and also satisfying randomness conservation: if F : 2 N ź 2 N is an almost-everywhere computable, measure-preserving map, and if x ź 2 N is random, then F ( x ) is random.
更多查看译文
关键词
Algorithmic randomness,Computable randomness (recursive randomness),Schnorr randomness,Randomness conservation (randomness preservation),No randomness from nothing (no randomness ex nihilo),Computable analysis
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络