Optical implementations of mathematical resolution

Abstract

Mathematical resolution is an algorithmic technique for reasoning from facts expressed in clause form to a conclusion. The technique is normally implemented on electronic computers with list-processing languages. This paper presents data representation and processing techniques for a parallel implementation using array-based optical logic. Implementations up through the quantified propositional calculus are presented, and the operations of resolvent formation, unification, and search are discussed. It is shown that a largely parallel formulation of resolution is possible, and optical technologies are suggested to implement this formulation.

Throughput enhancement for optical symbolic substitution computing systems

“…This is followed by a substitution phase whereby a different pattern is substituted in all the locations where the search pattern is found. SSL has been applied to a wide range of applications including digital logic and arithmetic operations, 4,5 signal and image processing, 6 -7 symbolic computing, 8,9 massively parallel computing, 10 implementation of artificial intelligence languages such as PROLOG, 11 and implementation of optical random access memory. 12 In all the implementations that have been reported for SSL thus far, the input operands are assumed to be placed vertically on top of each other so that the operands occupy distinct locations on the input plane.…”