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.
Keywords :
Affine equivalence, asymmetric switching functions, equivalence classes, exclusive-OR modules, logic design, logic networks, switching functions, symmetric switching functions.; Aerospace engineering; Algorithm design and analysis; Cellular networks; Graphics; Laboratories; Logic design; Network synthesis; Affine equivalence, asymmetric switching functions, equivalence classes, exclusive-OR modules, logic design, logic networks, switching functions, symmetric switching functions.;
