A. Nies

Publications
Influence

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

We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible. Expand

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 Computability: Open Questions

J. Miller, A. Nies
Mathematics, Computer Science
Bull. Symb. Log.
1 September 2006

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

A. Nies, R. Shore, T. Slaman
Mathematics
1 September 1998

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

We prove that any Chaitin Ω number (i.e., the halting probability of a universal self-delimiting Turing machine) is wtt-complete, but not tt-complete. Expand

Demuth randomness and computational complexity

A. Kucera, A. Nies
Mathematics, Computer Science
Ann. Pure Appl. Log.
1 June 2011

We show that a weakly Demuth random ∆02 set can be high and Δ20, yet not superhigh. Expand

Trivial Reals

R. Downey, Denis R. Hirschfeldt, A. Nies, F. Stephan
Computer Science
Electron. Notes Theor. Comput. Sci.
2002

We show that there are noncomputable reals α such that H(α n) 6 H(1n) + O(1) is prefix-free Kolmogorov complexity. Expand

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