Holzl, R and Shafer, PE orcid.org/0000-0001-5386-9218 (2015) Universality, optimality, and randomness deficiency. Annals of Pure and Applied Logic, 166 (10). pp. 1049-1069. ISSN 0168-0072
Abstract
A Martin-Löf test UU is universal if it captures all non-Martin-Löf random sequences, and it is optimal if for every ML-test VV there is a c∈ωc∈ω such that ∀n(Vn+c⊆Un)∀n(Vn+c⊆Un). We study the computational differences between universal and optimal ML-tests as well as the effects that these differences have on both the notion of layerwise computability and the Weihrauch degree of LAYLAY, the function that produces a bound for a given Martin-Löf random sequence's randomness deficiency. We prove several robustness and idempotence results concerning the Weihrauch degree of LAYLAY, and we show that layerwise computability is more restrictive than Weihrauch reducibility to LAYLAY. Along similar lines we also study the principle RDRD, a variant of LAYLAY outputting the precise randomness deficiency of sequences instead of only an upper bound as LAYLAY.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Elsevier Masson. This is an author produced version of a paper published in Annals of Pure and Applied Logic. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Universal Martin-Löf test; Optimal Martin-Löf test; Randomness deficiency; Layerwise computability; Weihrauch degrees |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Feb 2017 11:52 |
Last Modified: | 19 Jan 2018 07:39 |
Published Version: | https://doi.org/10.1016/j.apal.2015.05.006 |
Status: | Published |
Publisher: | Elsevier Masson |
Identification Number: | 10.1016/j.apal.2015.05.006 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111926 |