Probabilistic Resource Analysis by Program Transformation

The aim of a probabilistic resource analysis is to derive a probability distribution of possible resource usage for a program from a probability distribution of its input. We present an automated multi- phase rewriting based method to analyze programs written in a subset of C. It generates a probability distribution of the resource usage as a possibly uncomputable expression and then transforms it into a closed form expression using over-approximations. We present the technique, outline the implementation and show results from experiments with the system

On multivalued weakly Picard operators in partial Hausdorff metric spaces

We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces