Assumptions in the Threshold Synthesis of Symmetric Switching Functions

Abstract—This note establishes the fact that an optimal synthesis technique (even for a small number of variables) must abandon the basic assumption of assigning only +1 weights to the primary inputs. Examples are presented where both negative primary weights and/or nonunitary primary weights are required to achieve minimality. A method of network analysis is presented which leads to optimal synthesis in a significant number of new cases. The previously accepted lower bound on the number of devices needed to realize a symmetric function is questioned, and a proof is given to establish its validity. A previously published assertion about a least upper bound on the number of devices is shown to be incorrect.