An Approach for the Realization of Linearly-Separable Switching Functions

A distinct and straightforward method to test and realize linearly-separable switching functions is presented. This method makes use of a universal map which facilitates the generation of inequalities and the detection of contradictions. It also eliminates any preprocessing (such as positivizing and ordering) of a given function. The concept of composite level is first defined. A map is then developed, which is not restricted by the number of variables in the given function. A switching function can be easily mapped. A simple process is presented to generate inequalities by inspection. This process will either conclude that the given function is not linearly-separable or generate a set of composite levels and, consequently, a set of weights for the threshold switching device. Two illustrative examples are provided.