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- Publications
- Influence
Computability and randomness
- A. Nies
- Mathematics
- 2009
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The… Expand
Lowness properties and randomness
- A. Nies
- Mathematics
- 20 October 2005
Abstract The set A is low for (Martin-Lof) randomness if each random set is already random relative to A . A is K -trivial if the prefix complexity K of each initial segment of A is minimal, namely ∀… Expand
Randomness, relativization and Turing degrees
- A. Nies, F. Stephan, S. Terwijn
- Mathematics, Computer Science
- J. Symb. Log.
- 1 June 2005
TLDR
Using random sets as oracles
- Denis R. Hirschfeldt, A. Nies, F. Stephan
- Mathematics
- 1 June 2007
AbstractLet R be a notion of algorithmic randomness for individual subsets of ℕ. A set B is a base for R randomness if there is a Z ≥ T B such that Z is R random relative to B. We show that the bases… Expand
Randomness and Differentiability
- V. Brattka, J. Miller, A. Nies
- Mathematics, Computer Science
- ArXiv
- 22 April 2011
We characterize some major algorithmic randomness notions via differentiability of effective functions.
(1) As the main result we show that a real number z in [0,1] is computably random if and only… Expand
Interpretability and definability in the recursively enumerable degrees
We investigate definability in R, the recursively enumerable Turing degrees, using codings of standard models of arithmetic (SMA’s) as a tool. First we show that an SMA can be interpreted in R… Expand
Chaitin Numbers and Strong Reducibilities
- Cristian S. Calude, A. Nies
- Computer Science
- 1997
TLDR
- 47
- 9
- PDF
Demuth randomness and computational complexity
TLDR
Trivial Reals
- R. Downey, Denis R. Hirschfeldt, A. Nies, F. Stephan
- Computer Science
- Electron. Notes Theor. Comput. Sci.
- 2002
TLDR