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  1. Defining a randomness notion via another.Kojiro Higuchi & Ningning Peng - 2014 - Mathematical Logic Quarterly 60 (4-5):280-288.
    To compare two randomness notions with each other, we ask whether a given randomness notion can be defined via another randomness notion. Inspired by Yu's pioneering study, we formalize our question using the concept of relativization of randomness. We give some solutions to our formalized questions. Also, our results include the affirmative answer to the problem asked by Yu in a discussion with the second author, i.e., whether Schnorr randomness relative to the halting problem is equivalent to Martin‐Löf randomness relative (...)
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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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  • Algorithmic randomness and measures of complexity.George Barmpalias - 2013 - Bulletin of Symbolic Logic 19 (3):318-350.
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  • Algorithmic Randomness and Measures of Complexity.George Barmpalias - 2013 - Bulletin of Symbolic Logic 19 (3):318-350.
    We survey recent advances on the interface between computability theory and algorithmic randomness, with special attention on measures of relative complexity. We focus on reducibilities that measure the initial segment complexity of reals and 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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