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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.
Index terms?Bounds on complexity, optimal synthesis, symmetric metric functions, symmetric switching circuits, threshold logic.

M. Tannenbaum and M. Fischler, "Assumptions in the Threshold Synthesis of Symmetric Switching Functions," in IEEE Transactions on Computers, vol. 17, no. , pp. 273-279, 1968.
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