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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:
Index terms?Bounds on complexity, optimal synthesis, symmetric metric functions, symmetric switching circuits, threshold logic.
Citation:
M.A. Fischler, M. Tannenbaum, "Assumptions in the Threshold Synthesis of Symmetric Switching Functions," IEEE Transactions on Computers, vol. 17, no. 3, pp. 273-279, March 1968, doi:10.1109/TC.1968.229102
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