Towards Efficient Structural Analysis of Mathematical Expressions

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 Deenite Clause Grammar (DCG) as a formalism to deene a set of replacement rules for parsing mathematical expressions. With DCG, we are not only able to deene the replacement rules concisely, but their deenitions are also in a readily executable form. However, backtracking parsers like Pro-log interpreters, which execute DCG directly, are by nature ineecient. Thus we propose some methods here to increase the eeciency 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.