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Abstract?In this note, a class of switching functions, called threshold-product functions, whose definition is analogous to that of threshold functions (which will be called threshold-sum functions), is studied in detail. It is shown that both threshold functions and parity functions are special cases of threshold-product functions. A simple and economical threshold-logic realization method is established for threshold-product functions. This economical realization method is based on constrained solutions for threshold-product functions. A systematic technique for finding a constrained solution for a threshold-product function is obtained, and this technique can be employed for testing whether a switching function is a threshold-product function as well. When the number of variables in a switching function is not large, say no more than 6, a simpler method for the above purposes is found. Furthermore, a threshold-logic realization method which yields a minimal realization for certain threshold-product functions is obtained.
Index terms?Economical and minimal threshold-logic realizations: constrained solutions, techniques, and properties; parity functions, switching functions, threshold-logic networks, threshold-product functions, threshold-sum functions.
S.S. Yau, D.L. Ostapko, "Realization of a Class of Switching Functions by Threshold-Logic Networks", IEEE Transactions on Computers, vol. 17, no. , pp. 391-399, April 1968, doi:10.1109/TC.1968.229390
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