Abstract
The interrelationships among symbolic substitution, neural nets, optical correlators, the permutation group SN, 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 SN the interrelationships imply access to a powerful mathematical base for optical nets. A binary Grossberg model leads to a characterization of SN in terms of the number of nodes and input connections.
© 1987 Optical Society of America
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