Several new higher-order spatial symbol recognition methods for optical symbolic
substitution-based calculations are presented. In case of logic processing, higher-order
symbolic substitution (SS) rules can be applied to implement multi-variable logic functions.
In binary arithmetical calculations requiring carry propagation, the simultaneous processing
of a number of bits increases computational speed. Finally, using higher-order SS rules,
image processing can be perform using larger windows. Both, multiplicative and additive
techniques for a spatial symbol recognition are discussed. Four different optical architectures,
a multi-reflecting technique using an optical cavity, a correlation, a phase conjugation
and a content-addressable memory (CAM) techniques, are suggested. Optical either
dual-rail (DR) or triple-rail (TR) spatial encoding is employed. Some preliminary
experimental results are also included.