Structure and Term Prediction for Mathematical Text

Mathematical text is too cumbersome to write because of the need to encode a tree structure in a left to right linear order. This paper defines two novel problems, namely structure prediction from unstructured representation and sequence prediction within a mathematical session, to help address mathematical text entry. The effectiveness of our approach relies on the fact that normal mathematical text is highly symmetric. Our solution to the structure prediction problem involves defining a ranking measure that captures symmetry of a mathematical term, and an algorithm for efficiently finding the structure with the highest rank. Our solution to the sequence prediction problem involves defining a domain-specific language for term transformations, and an inductive synthesis algorithm that can learn the likely transformation from the first couple of sequence elements. Our tool is able to predict the correct structure in 63% of the cases, and save more then half of sequence typing time in 52% of the cases on our benchmark collection. We argue that such algorithms are important components of human-computer interfaces for inputting mathematical text, be it through speech, keyboard, touch or multimodal interfaces.