Symmetric Circuits and the Concept of Logical Potential

Symmetric circuits with more than one output can traditionally be reduced by shifting down if the outputs have certain properties. It is shown here that any nontrivial symmetric circuit can be shifted down using the method described. The reduction is made logical and simple to understand by means of the concept of logical potential, in which the circuit is diagrammed, and a "potential" assigned to each node in the diagram. The method shows which shifts are valid and avoids those which result in sneak circuits. It provides an excellent tutorial approach for classroom teaching of symmetric circuit reduction in courses on logic and switching circuit theory.