کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4661711 | 1633452 | 2015 | 16 صفحه PDF | دانلود رایگان |
Let X be an infinite sequence of 0's and 1's. Let f be a computable function. Recall that X is strongly f-random if and only if the a priori Kolmogorov complexity of each finite initial segment τ of X is bounded below by f(τ)f(τ) minus a constant. We study the problem of finding a PA-complete Turing oracle which preserves the strong f-randomness of X while avoiding a Turing cone. In the context of this problem, we prove that the cones which cannot always be avoided are precisely the K-trivial ones. We also prove: (1) If f is convex and X is strongly f-random and Y is Martin-Löf random relative to X, then X is strongly f-random relative to Y. (2) X is complex relative to some oracle if and only if X is random with respect to some continuous probability measure.
Journal: Annals of Pure and Applied Logic - Volume 166, Issue 6, June 2015, Pages 713–728