Verification of mathematical formulae based on a combination of context-free grammar and tree grammar

Akio Fujiyoshi, Masakazu Suzuki, Seiichi Uchida

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationIntelligent Computer Mathematics - 9th International Conference, AISC 2008 - 15th Symposium, Calculemus 2008 - 7th International Conference, MKM 2008, Proceedings
Pages415-429
Number of pages15
DOIs
Publication statusPublished - Sep 10 2008
Event9th Int. Conf. Artificial Intelligence and Symbolic Computation, AISC 2008 - 15th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2008 - 7th Int. Conf. Mathematical Knowledge Management, MKM 2008 - Birmingham, United Kingdom
Duration: Jul 28 2008Aug 1 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5144 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th Int. Conf. Artificial Intelligence and Symbolic Computation, AISC 2008 - 15th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2008 - 7th Int. Conf. Mathematical Knowledge Management, MKM 2008
CountryUnited Kingdom
CityBirmingham
Period7/28/088/1/08

Fingerprint

Context free grammars
Optical character recognition
Context-free Grammar
Grammar
Compiler
Output
Evaluation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Fujiyoshi, A., Suzuki, M., & Uchida, S. (2008). Verification of mathematical formulae based on a combination of context-free grammar and tree grammar. In Intelligent Computer Mathematics - 9th International Conference, AISC 2008 - 15th Symposium, Calculemus 2008 - 7th International Conference, MKM 2008, Proceedings (pp. 415-429). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5144 LNAI). https://doi.org/10.1007/978-3-540-85110-3_35

Verification of mathematical formulae based on a combination of context-free grammar and tree grammar. / Fujiyoshi, Akio; Suzuki, Masakazu; Uchida, Seiichi.

Intelligent Computer Mathematics - 9th International Conference, AISC 2008 - 15th Symposium, Calculemus 2008 - 7th International Conference, MKM 2008, Proceedings. 2008. p. 415-429 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5144 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Fujiyoshi, A, Suzuki, M & Uchida, S 2008, Verification of mathematical formulae based on a combination of context-free grammar and tree grammar. in Intelligent Computer Mathematics - 9th International Conference, AISC 2008 - 15th Symposium, Calculemus 2008 - 7th International Conference, MKM 2008, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5144 LNAI, pp. 415-429, 9th Int. Conf. Artificial Intelligence and Symbolic Computation, AISC 2008 - 15th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2008 - 7th Int. Conf. Mathematical Knowledge Management, MKM 2008, Birmingham, United Kingdom, 7/28/08. https://doi.org/10.1007/978-3-540-85110-3_35
Fujiyoshi A, Suzuki M, Uchida S. Verification of mathematical formulae based on a combination of context-free grammar and tree grammar. In Intelligent Computer Mathematics - 9th International Conference, AISC 2008 - 15th Symposium, Calculemus 2008 - 7th International Conference, MKM 2008, Proceedings. 2008. p. 415-429. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-85110-3_35
Fujiyoshi, Akio ; Suzuki, Masakazu ; Uchida, Seiichi. / Verification of mathematical formulae based on a combination of context-free grammar and tree grammar. Intelligent Computer Mathematics - 9th International Conference, AISC 2008 - 15th Symposium, Calculemus 2008 - 7th International Conference, MKM 2008, Proceedings. 2008. pp. 415-429 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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