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Demuth's Path to Randomness

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10126353" target="_blank" >RIV/00216208:11320/12:10126353 - isvavai.cz</a>

  • Result on the web

    <a href="http://link.springer.com/chapter/10.1007%2F978-3-642-27654-5_12" target="_blank" >http://link.springer.com/chapter/10.1007%2F978-3-642-27654-5_12</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/978-3-642-27654-5_12" target="_blank" >10.1007/978-3-642-27654-5_12</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Demuth's Path to Randomness

  • Original language description

    Osvald Demuth (1936-1988) studied constructive analysis in the Russian style. For this he introduced notions of effective null sets which, when phrased in classical language, yield major algorithmic randomness notions. He proved several results connecting constructive analysis and randomness that were rediscovered only much later. We give an overview in mostly chronological order. We sketch a proof that Demuth's notion of Denjoy sets (or reals) coincides with computable randomness. We show that he worked with a test notion that is equivalent to Schnorr tests relative to the halting problem. We also discuss the invention of Demuth randomness, and Demuth's and Kučera's work on semigenericity.

  • 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

    Lecture Notes in Computer Science

  • ISSN

    0302-9743

  • e-ISSN

  • Volume of the periodical

    7160

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    15

  • Pages from-to

    159-173

  • UT code for WoS article

  • EID of the result in the Scopus database