LOOP-FREE THRESHOLD ELEMENT STRUCTURES

The paper deals with the problem of “compound” and “cascade threshold” element “synthesis” of an arbitrary Boolean function from the “multithreshold weight threshold vector” (MTWTV). The above synthesis procedure is presented to reveal a unique feature of the multithreshold weight threshold vector, from which several realizations of threshold element nets can be obtained from one of the multithreshold weight threshold vectors. Specifically, two alternative forms of “compound threshold networks” are given, and a “cascade threshold network” is achieved free from constraints on the thresholds of the MTWTV. For the compound synthesis, Boolean functions of n variables can be realized with no more than three logic levels, and the number of logic levels needed for cascade threshold network synthesis is bounded by the number of thresholds in the MTWTV. The number of single threshold elements needed for the synthesis is bounded by the number of thresholds in the MTWTV for all of the realizations. An example is given to illustrate the synthesis procedure which requires no cut and try steps. Finally, threshold network structures corresponding to the 221 equivalence classes of 4-variable functions under the “NPN operations” have been tabulated. Copyright © 1969 by The Institute of Electrical and Electronics Engineers, Inc.