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ABSTRACT
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.
INDEX TERMS
Affine equivalence, asymmetric switching functions, equivalence classes, exclusive-OR modules, logic design, logic networks, switching functions, symmetric switching functions.
CITATION

C. Jackson and H. Stone, "Structures of the Affine Families of Switching Functions," in IEEE Transactions on Computers, vol. 18, no. , pp. 251-257, 1969.
doi:10.1109/T-C.1969.222638
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