• Publications
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Computability and randomness
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. TheExpand
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Lowness properties and randomness
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
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Randomness, relativization and Turing degrees
TLDR
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
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Using random sets as oracles
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 basesExpand
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Randomness and Computability: Open Questions
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Randomness and Differentiability
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 onlyExpand
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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 RExpand
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Chaitin Numbers and Strong Reducibilities
TLDR
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
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Demuth randomness and computational complexity
TLDR
We show that a weakly Demuth random ∆02 set can be high and Δ20, yet not superhigh. Expand
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Trivial Reals
TLDR
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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