Symbolic substitution and patterns
John L. Johnson · Annual Meeting Optical Society of America · 1987
The interrelationships among symbolic substitution, neural nets, optical correlators, the permutation group S N , and digital computers are discussed. An example is given showing how these apply to the design of a full binary adder. Arithmetic rules are transformed into two pattern replacement rules which are implemented by neural networks. These are combined to form the N-bit adder. A functionally equivalent system design using optical correlation techniques is discussed. The group aspect is discussed. Since every group is isomorphic to a subgroup of S N the interrelationships imply access to a powerful mathematical base for optical nets. A binary Grossberg model leads to a characterization of S N in terms of the number of nodes and input connections.