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

Akio Fujiyoshi; Masakazu Suzuki; Seiichi Uchida

doi:10.1007/978-3-540-85110-3_35

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

Akio Fujiyoshi, Masakazu Suzuki, Seiichi Uchida

Real world robotics

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Intelligent Computer Mathematics - 9th International Conference, AISC 2008 - 15th Symposium, Calculemus 2008 - 7th International Conference, MKM 2008, Proceedings
Pages	415-429
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-540-85110-3_35
Publication status	Published - Sept 10 2008
Event	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 Duration: Jul 28 2008 → Aug 1 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5144 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	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
Country/Territory	United Kingdom
City	Birmingham
Period	7/28/08 → 8/1/08

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-540-85110-3_35

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 proceeding › Conference 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)). doi: 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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Verification of mathematical formulae based on a combination of context-free grammar and tree grammar

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