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K-trivial, K-low and MLR-low sequences: a tutorial

Abstract : A remarkable achievement in algorithmic randomness and algorithmic information theory was the discovery of the notions of K-trivial, K-low and Martin-Lof-random-low sets: three different definitions turns out to be equivalent for very non-trivial reasons. This paper, based on the course taught by one of the authors (L.B.) in Poncelet laboratory (CNRS, Moscow) in 2014, provides an exposition of the proof of this equivalence and some related results. We assume that the reader is familiar with basic notions of algorithmic information theory.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01233787
Contributor : Alexander Shen <>
Submitted on : Wednesday, November 25, 2015 - 5:41:20 PM
Last modification on : Friday, March 27, 2020 - 3:50:35 AM

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Laurent Bienvenu, Alexander Shen. K-trivial, K-low and MLR-low sequences: a tutorial. Fields of Logic and Computation II, LNCS (9300), Springer, pp.1-23, 2015, Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday, 978-3-319-23533-2. ⟨10.1007/978-3-319-23534-9_1⟩. ⟨lirmm-01233787⟩

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