DEMUTH'S PATH TO RANDOMNESS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10312224" target="_blank" >RIV/00216208:11320/15:10312224 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/bsl.2015.24" target="_blank" >http://dx.doi.org/10.1017/bsl.2015.24</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/bsl.2015.24" target="_blank" >10.1017/bsl.2015.24</a>

Result language
angličtina
Original language name
DEMUTH'S PATH TO RANDOMNESS
Original language description
Osvald Demuth (1936-1988) studied constructive analysis from the viewpoint of the Russian school of constructive mathematics. In the course of his work he introduced various notions of effective null set which, when phrased in classical language, yield anumber of major algorithmic randomness notions. In addition, he proved several results connecting constructive analysis and randomness that were rediscovered only much later. In this paper, we trace the path that took Demuth from his constructivist roots to his deep and innovative work on the interactions between constructive analysis, algorithmic randomness, and computability theory. We will focus specifically on (i) Demuth's work on the differentiability of Markov computable functions and his study of constructive versions of the Denjoy alternative, (ii) Demuth's independent discovery of the main notions of algorithmic randomness, as well as the development of Demuth randomness, and (iii) the interactions of truth-table reducibility,
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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