Discussion of Some Flaws in the Classical Theory of Two-Level Minimization of Multiple-Output Switching Networks

Abstract—Two errors have been found in the classical theory of two-level minimization of multiple-output switching networks. First, the prime implicant theorem must be modified to cover certain degenerate cases, and second, the widely accepted notion that there can always be found a miinimal network corresponding to a set of equations that are entirely sum-of-products or entirely product-of-sums is incorrect in a less trivial way, viz., sometimes the minimal network corresponds to a mixed representation (a set of equations some of which are products-of-sums and the remainder of which are sums-of-products). Counter examples are displayed to support these claims. Networks are exhibited in which AND gates feed AND gates.