Probabilistic Output Analyses for Deterministic Programs --- Reusing Existing Non-probabilistic Analyses

We consider reusing established non-probabilistic output analyses (either forward or backwards) that yield over-approximations of a program's pre-image or image relation, e.g., interval analyses. We assume a probability measure over the program input and present two techniques (one for forward and one for backward analyses) that both derive upper and lower probability bounds for the output events. We demonstrate the most involved technique, namely the forward technique, for two examples and compare their results to a cutting-edge probabilistic output analysis.