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Autonomous vehicles (AVs) have already driven millions of miles on public roads, but even the simplest scenarios have not been certified for safety. Current methodologies for the verification of AV’s decision and control systems attempt to divorce the lower level, short-term trajectory planning and trajectory tracking functions from the behavioral rules-based framework that governs mid-term actions. Such analysis is typically predicated on the discretization of the state space and has several limitations. First, it requires that a conservative buffer be added around obstacles such that many feasible plans are classified as unsafe. Second, the discretized controllers modeled in this analysis require several refinement steps before being implementable on an actual AV, and typically do not allow the specification of comfort-related properties on the trajectories. Consumer-ready AVs use motion planning algorithms that generate smooth trajectories.

For many crucial applications, establishing important properties of Simulink models by testing is either extremely resource intensive or impossible, and proof of the properties is highly desirable. Many Simulink models rely upon discrete-valued functions for which the function values are defined as a lookup table of correspondences between values in the domain and range, with linear interpolation used to evaluate intermediate values in the domain. Such discrete-valued functions arise in applications for which no known closed-form algebraic definition exists. In general, the proof of a property for a model that includes a discrete-valued function has to be by case analysis. For a single function and with mechanical support, case analysis is manageable. However, for models that include multiple discrete-valued functions, the number of cases can be the product of the cardinalities of the domains of the individual functions.