An e$cient syntactic approach to structural analysis of on-line handwritten 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 de"nite clause grammar (DCG) as a formalism to de"ne a set of replacement rules for parsing mathematical expressions. With DCG, we are not only able to de"ne the replacement rules concisely, but their de"nitions are also in a readily executable form. However, a DCG parser is potentially ine$cient due to its frequent use of backtracking. Thus, we propose some methods here to increase the e$ciency of the parsing process. Experiments done on some commonly seen mathematical expressions show that our proposed methods can achieve quite satisfactory speedup, making mathematical expression recognition more feasible for real-world applications. ( 2000 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.