Demuth randomness and computational complexity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10100555" target="_blank" >RIV/00216208:11320/11:10100555 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.apal.2011.01.004" target="_blank" >http://dx.doi.org/10.1016/j.apal.2011.01.004</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apal.2011.01.004" target="_blank" >10.1016/j.apal.2011.01.004</a>

Result language
angličtina
Original language name
Demuth randomness and computational complexity
Original language description
Demuth tests generalize Martin-Lof tests (G(m))(m epsilon N) in that one can exchange the m-th component a computably bounded number of times. A set Z subset of N fails a Demuth test if Z is in infinitely many final versions of the G(m). If we only allowDemuth tests such that G(m) superset of G(m+1) for each m, we have weak Demuth randomness. We show that a weakly Demuth random set can be high and Delta(0)(2) yet not superhigh. Next, any c.e. set Turing below a Demuth random set is strongly jump-traceable. We also prove a basis theorem for non-empty Pi(0)(1) classes P. It extends the Jockusch-Soare basis theorem that some member of P is computably dominated. We use the result to show that some weakly 2-random set does not compute a 2-fixed point freefunction.
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
JC - Computer hardware and software
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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