\(L^1\)-computability, layerwise computability and Solovay reducibility (Q2851186)
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scientific article; zbMATH DE number 6214532
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^1\)-computability, layerwise computability and Solovay reducibility |
scientific article; zbMATH DE number 6214532 |
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10 October 2013
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algorithmic randomness
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computable analysis
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\(L^1\)-computability
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layerwise computability
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Solovay reducibility
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0.8806354
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0.8660922
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0.8630209
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0.8628083
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0.86244357
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0.8617098
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0.8599797
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\(L^1\)-computability, layerwise computability and Solovay reducibility (English)
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In this paper, the author studies how several notions of randomness relate to classes of functions. The notions of randomness which are considered in this paper are: weak 2-randomness, Martin-Löf randomness, Schnorr randomness and Kurtz randomness. These randomness notions are characterized in several ways. In particular, weak 2-randomness and Schnorr randomness are characterized via integral tests. The author also relates several notions of \(L^1\)-computability to the difference of two integral tests for Schnorr randomness, for Martin-Löf randomness, and for weak 2-randomness. Solovay reducibility for lower semicomputable functions is also considered as well as its connections to the randomness notions mentioned above.
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