Mathematics recognition using graph rewriting

Abstract

This paper investigates graph rewriting as a tool for high-level recognition of two-dimensional mathematical notation. "High-level recognition" is the process of determining the meaning of a diagram from the output of a symbol recognizer. Characteristic problems of high-level mathematics recognition include: determining the groupings of symbols into recursive subexpressions and resolving ambiguities that depend upon global context. Our graph-rewriting approach uses knowledge of the notational conventions of mathematics, such as operator precedence and operator range, more effectively than syntactic or previous structural methods. Graph rewriting offers a flexible formalism with a strong theoretical foundation for manipulating two-dimensional patterns. It has been shown to be a useful technique for high-level recognition of circuit diagrams and musical scores. By demonstrating a graph-rewriting strategy for mathematics recognition, this paper provides further evidence for graph rewriting as a general tool for diagram recognition, and identifies some of the issues that must be considered as this potential is explored.