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
and the correct sequence in 63% and 65% of the cases respectively 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.