Digital optical computing with Symbolic Substitution.

The innate parallelism of optics makes it difficult to perform sequential operation. Symbolic Substitution Logic, a spatial transformation, in which one pattern is substituted for another, is proposed as a paralled mechanism capable of supporting sequential operations. An optical implementation based on on splitting an image, shifting the split images, superimposing the results, regenerating the superimposed image with an optical logic array, splitting the regenerated image, shifting the resulting images, and superimposing the shifted images is proposed. Some early experimental results are shown. Examples showing how Symbolic Substitution can be used to implement Boolean logic, binary arithmetic, cellular logic, and simple Turing machines are also presented.