Symbolic Substitution Methods For Optical Computing

Abstract

Symbolic substitution is a method of computing based on parallel binary pattern replacement, that can be implemented with simple optical components and regular free-space interconnection schemes. A two-dimensional pattern is searched for in parallel in an array and is replaced with another pattern. Pattern transformation rules can be applied sequentially or in parallel to realize complex functions. When the substitution space is modified to be loge SIT connected for N binary spots, and masks are allowed to customize the system, then optical digital circuits using symbolic substitution for network interconnects can be made nearly as efficient in terms of gate count and circuit depth as conventional arbitrary interconnection schemes allow. We describe an optical setup that requires no more than a fanin and fanout of two using optically nonlinear logic devices and a free space interconnection scheme based on symbolic substitution.