2010
DOI: 10.1007/978-3-642-15240-5_19
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Initial Segment Complexities of Randomness Notions

Abstract: Abstract. Schnorr famously proved that Martin-Löf-randomness of a sequence A can be characterised via the complexity of A's initial segments. Nies, Stephan and Terwijn as well as independently Miller showed that Kolmogorov randomness coincides with Martin-Löf randomness relative to the halting problem K; that is, a set A is Martin-Löf random relative to K iff there is no function f such that for all m andIn the present work it is shown that characterisations of this style can also be given for other randomness… Show more

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