Loïc Pottier

On-line handwritten formula recognition using hidden Markov models and context dependent graph grammars

This paper presents an approach for the recognition of on-line handwritten mathematical expressions. The hidden Markov model (HMM) based system makes use of simultaneous segmentation and recognition capabilities, avoiding a crucial segmentation during pre-processing. With the segmentation and recognition results, obtained from the HMM recognizer it is possible to analyze and interpret the spatial two-dimensional arrangement of the symbols. We use a graph grammar approach for the structure recognition, also used in off-line recognition process, resulting in a general tree-structure of the underlying input-expression. The resulting constructed tree can be translated to any desired syntax (for example: Lisp, KT/sub E/X, and OpenMath).

Proof certificates for algebra and their application to automatic geometry theorem proving

Integrating decision procedures in proof assistants in a safe way is a major challenge. In this paper, we describe how, starting from Hilberts Nullstellensatz theorem, we combine a modified version of Buchbergers algorithm and some reflexive techniques to get an effective procedure that automatically produces formal proofs of theorems in geometry. The method is implemented in the Coq system but, since our specialised version of Buchbergers algorithm outputs explicit proof certificates, it could be easily adapted to other proof assistants.

Mathematical formula recognition using graph grammar

This paper describes current results of Ofr, a system for extracting and understanding mathematical expressions in documents. Such a tool could be really useful to be able to re-use knowledge in scientific books which are not available in electronic form. We currently also study use of this system for direct input of formulas with a graphical tablet for computer algebra system softwares. Existing solutions for mathematical recognition have problems to analyze 2D expressions like vectors and matrices. This is because they often try to use extended classical grammar to analyze formulas, relatively to baseline. But a lot of mathematical notations do not respect rules for such a parsing and that is the reason why they fail to extend text parsing technic. We investigate graph grammar and graph rewriting as a solution to recognize 2D mathematical notations. Graph grammar provide a powerful formalism to describe structural manipulations of multi-dimensional data. The main two problems to solve are ambiguities between rules of grammar and construction of graph.