10 citations · 29 across the 12 of their papers we have counts for
12 papers
Local time of Martin-Lof Brownian motion
Willem Fouche, Safari Mukeru
In this paper we study the local times of Brownian motion from the point of view of algorithmic randomness. We introduce the notion of effective local time and show that any path w…
Randomized Computation of Continuous Data: Is Brownian Motion Computable?
Willem Fouché, Hyunwoo Lee, Donghyun Lim +3
We consider randomized computation of continuous data in the sense of Computable Analysis. Our first contribution formally confirms that it is no loss of generality to take as samp…
Weihrauch-completeness for layerwise computability
Arno Pauly, Willem Fouché, George Davie
We introduce the notion of being Weihrauch-complete for layerwise computability and provide several natural examples related to complex oscillations, the law of the iterated logari…
How constructive is constructing measures?
Arno Pauly, Willem L. Fouché
Given some set, how hard is it to construct a measure supported by it? We classify some variations of this task in the Weihrauch lattice. Particular attention is paid to Frostman m…
Diophantine properties of Brownian motion: recursive aspects
Willem L. Fouche
We use recent results on the Fourier analysis of the zero sets of Brownian motion to explore the diophantine properties of an algorithmically random Brownian motion (also known as…
Kolmogorov complexity and the geometry of Brownian motion
Willem L. Fouche
In this paper, we continue the study of the geometry of Brownian motions which are encoded by Kolmogorov-Chaitin random reals (complex oscillations). We unfold Kolmogorov-Chaitin c…
Fourier spectra of measures associated with algorithmically random Brownian motion
Willem Louw Fouché, Safari Mukeru, George Davie
In this paper we study the behaviour at infinity of the Fourier transform of Radon measures supported by the images of fractal sets under an algorithmically random Brownian motion.…
Algorithmic randomness and Ramsey properties of countable homogeneous structures
Willem L. Fouché
We study, in the context of algorithmic randomness, the closed amenable subgroups of the symmetric group of a countable set. In this paper we address this problem by inv…
Martin-Lof randomness, invariant measures and countable homogeneous structurs
Willem L. Fouche
We use ideas from topological dynamics (amenability), combinatorics (structural Ramsey theory) and model theory (Fra\" {i}ss\' e limits) to study closed amenable subgroups of t…
Universality and programmability of quantum computers
Willem Fouche', Johannes Heidema, Glyn Jones +1
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing…
Halting in quantum Turing computation
W. L. Fouché, J. Heidema, G. Jones +1
The paper considers the halting scheme for quantum Turing machines. The scheme originally proposed by Deutsch appears to be correct, but not exactly as originally intended. We disc…
Kolmogorov complexity and symmetric relational structures
W. L. Fouché, P. H. Potgieter
We study partitions of Fra\"ıssé limits of classes of finite relational structures where the partitions are encoded by infinite binary sequences which are random in the sense of Ko…