Two long-open problems have been solved: (1) every sufficiently large planar point set in general position contains the vertices of an empty hexagon; (2) every finite collection o...
There are many ways to define complexity in logic. In finite model theory, it is the complexity of describing properties, whereas in proof complexity it is the complexity of provin...
Title of dissertation: MODEL THEORY AND COMPLEXITY THEORY Walid Gomaa Doctor of Philosophy, 2007 Dissertation directed by: Professor William Gasarch Department of Computer Science...
We establish a new connection between the two most common traditions in the theory of real computation, the Blum-Shub-Smale model and the Computable Analysis approach. We then use...
The localization of critical parameter sets called bifurcations is often a central task of the analysis of a nonlinear dynamical system. Bifurcations of codimension 1 that can be ...