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A novel parallel model of natural language (NL) understanding is presented which can realize high levels of semantic abstraction, and is designed for implementation on synchronous SIMD architectures and optical processors. Theory is expressed in terms of the Image Algebra (IA), a rigorous, concise, inherently parallel notation which unifies the design, analysis, and implementation of image processing algorithms. The IA has been implemented on numerous parallel architectures, and IA preprocessors and interpreters are available for the FORTRAN and Ada languages. In a previous study, we demonstrated the utility of IA for mapping MEA- conformable (Multiple Execution Array) algorithms to optical architectures. In this study, we extend our previous theory to map serial parsing algorithms to the synchronous SIMD paradigm. We initially derive a two-dimensional image that is based upon the adjacency matrix of a semantic graph. Via IA template mappings, the operations of bottom-up parsing, semantic disambiguation, and referential resolution are implemented as image-processing operations upon the adjacency matrix. Pixel-level operations are constrained to Hadamard addition and multiplication, thresholding, and row/column summation, which are available in magnitude-only optics. Assuming high parallelism in the parse rule base, the parsing of n input symbols with a grammar consisting of M rules of arity H, on an N-processor architecture, could exhibit time complexity of T(n) <EQ O(MHn/N). When N equals O (Mn), which is feasible with massive parallelism, the computational cost is constant and of order H. Since H < < n is typical, we claim a fundamental complexity advantage over the current O(n) theoretical time limit of MIMD parsing architectures. Additionally, we show that inference over a semantic net is achievable is parallel in O(m) time, where m corresponds to the depth of the search tree. Results are evaluated in terms of computational cost on SISD and SIMD processors, with discussion of implementation on electro-optic architectures.
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