Properties and Transformations of Single Threshold Element Functions

A large number of Boolean functions may be realized as the output of a single threshold element; however, not all functions are so realizable. Those Fn which are, are said to belong to the class R. No easily applicable criteria have been formulated which enable an unequivocal determination to be made of whether a given Fn¿ R. There are, however, certain transformations allowable on those Fn¿ R which exhibit a closure property, that is, the transformation results in an Fp¿ R. There are also certain properties of the form of Fn¿ R which can be recognized easily. A knowledge of these permissible transformations and observations of the form of a given Fn will, in many instances, allow for the desired. determination. This paper, for the most part, examines those permissible transformations and properties of form.