Propagation of partial randomness

Kojiro Higuchi; W. M. Phillip Hudelson; Stephen G. Simpson; Keita Yokoyama

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arXiv · 1311.0724

Propagation of partial randomness

Kojiro Higuchi·W. M. Phillip Hudelson·Stephen G. Simpson·Keita Yokoyama

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Abstract

Let f be a computable function from finite sequences of 0's and 1's to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-L"of random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f-randomness relative to a PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree.

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BibTeX RIS

Kojiro Higuchi, W. M. Phillip Hudelson, Stephen G. Simpson, Keita Yokoyama. 2013-11-04. Propagation of partial randomness. https://arxiv.org/abs/1311.0724

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