Iterative Switching Networks Composed of Combinational Cells

The networks considered in this paper consist of n identical combinational logic cells connected in cascade through bi-directional discrete information channels. All switching is done synchronously with unit time delay through each cell. Three classes of networks are formed according to whether or not information flow in one direction along the cascade is dependent upon that in the other. Steady-state behavioral relationships between the three classes are discussed, and the class having mutually dependent information flow is shown to be the only one which can exhibit steady-state memory properties. The main object of the paper is to derive several theorems concerning these memory properties. The last section interprets some previous results of Hennie as a start on the transients and cycling problems.