The aim of this study is to introduce a formal framework for analysis and synthesis of driver assistance systems. It applies formal methods to the verification of a stochastic human driver model built using the cognitive architecture ACT-R, and then bootstraps safety in semi-autonomous vehicles through the design of provably correct Advanced Driver Assistance Systems. The main contributions include the integration of probabilistic ACT-R models in the formal analysis of semi-autonomous systems and an abstraction technique that enables a finite representation of a large dimensional, continuous system in the form of a Markov model. The effectiveness of the method is illustrated in several case studies under various conditions.