Verification of Mathematical Formulae Based on a Combination of Context-Free Grammar and Tree Grammar

Authors:
Akio Fujiyoshi;Masakazu Suzuki;Seiichi Uchida
Affiliations:
Department of Computer and Information Sciences, Ibaraki University,;Faculty of Mathematics, Kyushu University,;Faculty of Information Science and Electrical Engineering, Kyushu University,
Venue:
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Year:
2008

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Abstract

This paper proposes the use of a formal grammar for the verification of mathematical formulae for a practical mathematical OCR system. Like a C compiler detecting syntax errors in a source file, we want to have a verification mechanism to find errors in the output of mathematical OCR. Linear monadic context-free tree grammar (LM-CFTG) was employed as a formal framework to define "well-formed" mathematical formulae. For the purpose of practical evaluation, a verification system for mathematical OCR was developed, and the effectiveness of the system was demonstrated by using the ground-truthed mathematical document database INFTY CDB-1.