Regular expressions in the mathematical text recognition problem

The work is devoted to use of regular expressions at recognition of hand-written mathematic texts. The main problem in handwritten mathematical formula recognition is that these texts mainly consist of a large number of small fragments, arranged in accordance with some strict rules. Despite the fact that formal definition of syntax of mathematic texts can involve context-free grammars and even more complicated constructions, it frequently suffices definition of mathematical language on the base of regular expressions for successful recognition. Since some constructions can occur in mathematic texts frequently than other, we introduce the concept of the weighed regular expression. The weights determine preference of some constructions before other ones. In the work, mathematical tools for use of such expressions at recognition is introduced. Theorems about intersection of weighed sets defined by such regular expressions are proved. Some estimations are given to complexity of algorithms work using such regular expressions for recognition.