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The equivalence relation that partitions switching functions into affine families leads to a natural graphic representation of the families. From the graphs, it is possible to derive information on the self-symmetries of switching functions and the relative symmetries of functions that are in the same family. A catalog of the structures of the 39 families of four-variable functions appears in the paper. The catalog and, more generally, the theory of affine equivalence are useful tools for the design of logic networks that contain exclusive-OR modules among the set of primitive building blocks.
Affine equivalence, asymmetric switching functions, equivalence classes, exclusive-OR modules, logic design, logic networks, switching functions, symmetric switching functions.
C.L. Jackson, H.S. Stone, "Structures of the Affine Families of Switching Functions", IEEE Transactions on Computers, vol. 18, no. , pp. 251-257, March 1969, doi:10.1109/T-C.1969.222638
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