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. We have observed production models in which this product rises to a level in which proof is intractable using standard techniques.
In this paper, we examine four approaches to dealing with the combinatorial explosion: parallelism, pruning, approximation with flat-interpolated lookup tables, and functional approximation. For each approach, we discuss the concept and present a preliminary analysis of performance.