A functional correspondence is shown among neural networks, symbolic substitution, digital computers, the permutation group SN, and optical correlator devices. Group and element networks are postulated. The dimensionality of the group number N is interpreted as a measure of the parallel capacity of a network. The principle of symbolic substitution is used to design S2 rules for a full binary adder, and neural model techniques are applied to produce a neural net implementing the adder. Optical neuromorphs are described for the processing nodes of the network.
John L. Johnson, "Architectural relationships involving symbolic substitution," Appl. Opt. 27, 529-533 (1988)