Towards efficient structural analysis of mathematical expressions

Abstract

Machine recognition of mathematical expressions is not trivial even when all the individual characters and symbols in an expression can be recognized correctly. In this paper, we propose to use Definite Clause Grammar (DCG) as a formalism to define a set of replacement rules for parsing mathematical expressions. With DCG, we are not only able to define the replacement rules concisely, but their definitions are also in a readily executable form. However, backtracking parsers like Prolog interpreters, which execute DCG directly, are by nature inefficient. Thus we propose some methods here to increase the efficiency of the parsing process. Experiments done on some typical mathematical expressions show that our proposed methods can achieve speedup ranging from 10 to 70 times, making mathematical expression recognition more feasible for real-world applications.