The Necessity of Closed Circuit Loops in Minimal Combinational Circuits

A cellular-logic approach is used to generate a family of multiple-output combinational switching circuits containing closed loops ( of the type that normally generate sequential behavior) and composed of simple gates. These networks contain fewer gates than any loop-free realizations. Some members of the family are oscillatory, while others are stable with multiple stable states, but the outputs remain quiescent in both cases. This result appears to have repercussions on some of the well-known optimality results of switching theory.