Algorithmic randomness and measures of complexity

Association for Symbolic Logic: The Bulletin of Symbolic Logic (forthcoming)
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We survey recent advances on the interface between computability theory and algorithmic randomness, with special attention on measures of relative complexity. We focus on (weak) reducibilities that measure (a) the initial segment complexity of reals and (b) the power of reals to compress strings, when they are used as oracles. The results are put into context and several connections are made with various central issues in modern algorithmic randomness and computability



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Kolmogorov complexity and computably enumerable sets.George Barmpalias & Angsheng Li - 2013 - Annals of Pure and Applied Logic 164 (12):1187-1200.

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