Recognition of Monotonic and Unate Cascade Realizable Functions Using an Informational Model of Switching Circuits

A model of combinational switching circuits used as information processors is described. A set of entropies (in the information theory sense) can be associated with each completely specified function, and can be easily computed from the truth table representation for the function. It is shown that simple arithmetic relations between the magnitudes of these entropies are sufficient to identify monotonic and unate functions and functions realizable as a unate cascade. In the latter case, a simple test identifies unate cascade realizable functions and gives the set of possible orderings of variables in the realization.