Prof W L Fouché

Tuition

Combinatorial Optimisation
Heuristics
Stochastics

Research

Application of stochastic processes to the understanding of complexity issues in fractal geometry and computability theory.
Ramsey theory and its links to dynamical systems.

Selected publications

WL Fouché, Fractals generated by algorithmically random Brownian motion, K. Ambos-Spies, B. Löwe, and W. Merkle (Eds.): CiE 2009, Lecture Notes in Computer Science vol 5635, Springer-Verlag, (2009), 208-217.

WL Fouché,  Subrecursive complexity of identifying the Ramsey structure of posets In: Logic and Theory of Algorithms, A Beckmann, C Dimitrapoulos, B Löwe (eds.), Lecture Notes in Theoretical Computer Science vol 5028, Springer-Verlag, (2008), 196-205.

WL Fouché, Dynamics of a generic Brownian motion: Recursive aspects. Theoretical Computer Sciences 394A (2008), 175-186.

WL Fouché, An Algorithmic Construction of Quantum Circuits of High Descriptive Complexity. Electronic Notes in Theoretical Computer Science 221 (2008), 61-69.

WL Fouché, Heidema, J., Jones, G., & Potgieter, P. H. (2008). Universality and programmability of quantum computers. Theoretical Computer Science, 403, 121-129.

WL Fouché, Jones, E. G., Heidema, J., & Potgieter, P. (2008). 'n Universele programmeerbare kwantumrekenaar? Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie, 27(3), 196–215.

WL Fouché, Heidema, J., Jones, G., & Potgieter, P. H. (2007). Halting in quantum Turing computation. In conference Unconventional Computing 2007; proceedings published as Unconventional Computing 2007 (Eds: Adamatzky e.a., Luniver Press), ISBN:190598605X.

WL Fouché, Brownian motion and Kolmogorov complexity, to appear in: Logical Approaches to Computational Barriers, University of Wales Swansea, Computer Science Report Series Arnold Beckmann, Ulrich Berger, Benedikt Lwe, & John V Tucker (eds.), (2006).

WL Fouché, L Pretorius & C Swanepoel, The Ramsey degrees of bipartite graphs: A primitive recursive proof, Discrete Math, 292 (2005).

WL Fouché, LM Pretorius & CJ Swanepoel, Partitions of factorisations of parameter words, Discrete Mathematics 231 (2001), 169--175.

WL Fouché, Discrepancies of hypergraphs of high Kolmogorov complexity, Journal of Combinatorial Mathematics and Combinatorial Computing 33 (2000), 199--207.

WL Fouché, The descriptive complexity of Brownian motion, Advances in Mathematics 155 (2000), 317--343.

WL Fouché, LM Pretorius & CJ Swanepoel Partition theorems for factorisations of ascending parameter words, Discrete Mathematics 197/198 (1999), 331--350.

WL Fouché, & Arithmetical representations of Brownian motion I, J Symbolic Logic 65 (2000), 421--442.