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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chan, K.F., Yeung, D.Y.: Mathematical expression recognition: a survey. Int. J. Document Analysis and Recoginition 3(1), 3–15 (2000)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison Wesley, Reading (1979)
Fujiyoshi, A., Kasai, T.: Spinal-formed context-free tree grammars. Theory of Computing Systems 33(1), 59–83 (2000)
Anderson, R.: Syntax-directed recognition of hand-printed two-dimensional mathematics. In: Interactive Systems for Experimental Applied Mathematics, pp. 436–459. Academic Press, London (1968)
Chou, P.A.: Recognition of equations using a two-dimensional stochastic context-free grammar. In: Proc. SPIE, vol. 1199, pp. 852–863 (1989)
Kanahori, T., Sexton, A., Sorge, V., Suzuki, M.: Capturing abstract matrices from paper. In: Borwein, J.M., Farmer, W.M. (eds.) MKM 2006. LNCS (LNAI), vol. 4108, pp. 124–138. Springer, Heidelberg (2006)
Suzuki, M., Uchida, S., Nomura, A.: A ground-truthed mathematical character and symbol image database. In: Proceedings of the 8th International Conference on Document Analysis and Recognition (ICDAR 2005), vol. 2, pp. 675–679 (2005)
Fujiyoshi, A.: Application of the CKY algorithm to recognition of tree structures for linear, monadic context-free tree grammars. IEICE Trans. Inf. & Syst. E90-D(2), 388–394 (2007)
Sikkel, K., Nijholt, A.: Parsing of Contex-Free Languages. In: Handbook of Formal Languages, vol. 2, pp. 61–100. Springer, Heidelberg (1997)
Suzuki, M., Tamari, F., Fukuda, R., Uchida, S., Kanahori, T.: Infty - an integrated OCR system for mathematical documents. In: Proceedings of ACM Symposium on Document Engineering 2003, pp. 95–104 (2003)
Infty Project, http://www.inftyproject.org/en/
Donnelly, C., Stallman, R.: Bison: The yacc-compatible parser generator (2006), http://www.gnu.org/software/bison/manual/
Mozilla Firefox, http://www.mozilla.com/firefox/
Fujiyoshi, A.: Analogical conception of chomsky normal form and greibach normal form for linear, monadic context-free tree grammars. IEICE Trans. Inf. & Syst. E89-D(12), 2933–2938 (2006)
Joshi, A.K., Levy, L.S., Takahashi, M.: Tree adjunct grammars. J. Computer & System Sciences 10(1), 136–163 (1975)
Joshi, A.K., Schabes, Y.: Tree-adjoining grammars. In: Handbook of Formal Languages, vol. 3, pp. 69–124. Springer, Berlin (1997)
Abeillé, A., Rambow, O. (eds.): Tree adjoining grammars: formalisms, linguistic analysis and processing. CSLI Publications, Stanford (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fujiyoshi, A., Suzuki, M., Uchida, S. (2008). Verification of Mathematical Formulae Based on a Combination of Context-Free Grammar and Tree Grammar. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85110-3_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-85110-3_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85109-7
Online ISBN: 978-3-540-85110-3
eBook Packages: Computer ScienceComputer Science (R0)