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K-Triviality, Oberwolfach Randomness, and Differentiability

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10126358" target="_blank" >RIV/00216208:11320/12:10126358 - isvavai.cz</a>

  • Result on the web

    <a href="http://www.mfo.de/scientific-programme/publications/owp/2012/OWP2012_17.pdf" target="_blank" >http://www.mfo.de/scientific-programme/publications/owp/2012/OWP2012_17.pdf</a>

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    K-Triviality, Oberwolfach Randomness, and Differentiability

  • Original language description

    We show that a Martin-Lof random set for which the effective version of the Lebesgue density theorem fails computes every K-trivial set. Combined with a recent result by Day and Miller, this gives a positive solution to the ML-covering problem (Question4.6 in Randomness and computability: Open questions. Bull. Symbolic Logic, 12(3):390-410, 2006). On the other hand, we settle stronger variants of the covering problem in the negative. We show that any witness for the solution of the covering problem, namely an incomplete random set which computes all K-trivial sets, must be very close to being Turing complete. For example, such a random set must be LR-hard. Similarly, not every K-trivial set is computed by the two halves of a random set. The work passes through a notion of randomness which characterises computing K-trivial sets by random sets. This gives a smart" K-trivial set, all randoms from whom this set is computed have to compute all K-trivial sets.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    IN - Informatics

  • OECD FORD branch

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2012

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Oberwolfach Preprints

  • ISSN

    1864-7596

  • e-ISSN

  • Volume of the periodical

    2012

  • Issue of the periodical within the volume

    17

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    40

  • Pages from-to

    1-40

  • UT code for WoS article

  • EID of the result in the Scopus database