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On Symmetric Functions with Redundant Variables?Weighted Functions
May 1973 (vol. 22 no. 5)
pp. 450-458
B. Dahlberg, Systems Engineering Laboratories, Inc.
Any switching function may be transformed into a completely symmetric switching function with some of its variables repetitive. In this paper we shall discuss certain properties, easily detectable in decomposition charts, that may be applied to reduce the number of repeated variables when such a transformation is performed. An algorithm utilizing lookup tables based on these properties has been devised enabling us with relative ease to transform an arbitrary switching function of four variables into a completely symmetric switching function with the least number of variables. The algorithm may be generalized to n-variable switching functions provided that the corresponding lookup tables are made available.
Index Terms:
Decomposition charts, lookup tables, multithreshold threshold logic, symmetric switching functions, symmetric switching functions with redundant variables, threshold logic.
Citation:
B. Dahlberg, "On Symmetric Functions with Redundant Variables?Weighted Functions," IEEE Transactions on Computers, vol. 22, no. 5, pp. 450-458, May 1973, doi:10.1109/T-C.1973.223747
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