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Reseach Article

Expanded Grammar for Detecting Equivalence in Math Expressions

by Mohammed Q. Shatnawi, Marwan T. Alquran, Fatima M. Quiam
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 43 - Number 15
Year of Publication: 2012
Authors: Mohammed Q. Shatnawi, Marwan T. Alquran, Fatima M. Quiam
10.5120/6183-8613

Mohammed Q. Shatnawi, Marwan T. Alquran, Fatima M. Quiam . Expanded Grammar for Detecting Equivalence in Math Expressions. International Journal of Computer Applications. 43, 15 ( April 2012), 44-51. DOI=10.5120/6183-8613

@article{ 10.5120/6183-8613,
author = { Mohammed Q. Shatnawi, Marwan T. Alquran, Fatima M. Quiam },
title = { Expanded Grammar for Detecting Equivalence in Math Expressions },
journal = { International Journal of Computer Applications },
issue_date = { April 2012 },
volume = { 43 },
number = { 15 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 44-51 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume43/number15/6183-8613/ },
doi = { 10.5120/6183-8613 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:33:32.263442+05:30
%A Mohammed Q. Shatnawi
%A Marwan T. Alquran
%A Fatima M. Quiam
%T Expanded Grammar for Detecting Equivalence in Math Expressions
%J International Journal of Computer Applications
%@ 0975-8887
%V 43
%N 15
%P 44-51
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Huge amount of different types of information are being posted on the web on a daily basis; therefore, searching capabilities should be provided to help users in finding their requested information. Locating a specific type of information within large repositories of disparate data becomes difficult, if not impossible, without specialized information retrieval systems. Traditional or text-based search engines do not achieve the level of success that users seek in retrieving structured information (e. g. mathematical information). For example, when a user searches for x(y+z) using Google, Google retrieves documents that contain xyz, x+y=z, (x+y+z) =xyz or any other document that contains x, y, and/or z, but not x(y+z) as a standalone expression. The reason behind this is that Google uses the text-based search capabilities/ Algorithms that depend, mostly, on techniques for matching and probabilities of occurrences of x, y, and z. The major obstacle of math search in current text search systems is that those systems do not differentiate between a user query that contains a mathematical expression, and any other query that contains text terms. Therefore, those text-based search systems process mathematical expressions as other texts, regardless of its nature whether being well-structured or not. Here in this context, the text search process will be refined to be applicable in searching for a mathematical expression by implementing a system that is responsible for detecting equivalent math expressions. In fact, more algorithms will be added to the Information Retrieval System in order to make it suitable to do search for a mathematical expression as well as other forms of text.

References
  1. Weglarz G. Two Worlds of Data – Unstructured and Structured, DM REVIEW MAGAZINE. http://www. dmreview. com/article. [accessed, March 2012].
  2. Kowalski, Gerald J. , Maybury, Mark T. "Information Storage and Retrieval Systems: Theory and Implementation", Springer, 2nd edition, 2000.
  3. Adeel M , Cheung H S and Khiyal S. "MATH GO! PROTOTYPE OF ACONTENT BASED MATHEMATICAL FORMULA SEARCH ENGINE". Journal of Theoretical and Applied Information Technology, 2008.
  4. Sergey Brin and Lawrence Page, "The Anatomy of a Large- Scale Hypertextual Web Search Engine", Proceedings of the 7th international conference on World Wide Web, Brisbane,Australia, 1998
  5. Mohammed Shatanwi, Abdou Youssef, "Equivalence Detection Using Parse-tree Normalization for Math Search ", ICDIM 2007 Lyon-France Oct 28-31-2007.
  6. Earl W. Swokowski, Michael Olinick, Dennis Pence "Calculus", Pws Pub. Co. , Sixth edition, 1994.
  7. Derivations and Parse Trees, http://www. cs. nuim. ie/~jpower/Courses/parsing/node24. html , [accessed February 2012]
  8. Miller B and Youssef A. Technical aspects of the Digital Library of Mathematical Functions. In: Annals of Mathematics and Artificial Intelligence; 2003; 38,121-136.
  9. World Wide Web Consortium. Mathematical Markup Language (MathML), http://www. w3. org/TR/MathML2. html Version2. 0. [accessed, January 2012]
  10. The OpenMath Society. OpenMath, http://www. openmath. org/society/index. html [accessed March 2012]
  11. Kohlhase M. OMDoc: An Open Markup Format for Mathematical Documents, http://www. mathweb. org/omdoc/pubs/omdoc1. 2. pdf [accessed December 2011]
  12. Altamimi M and Youssef A. A more canonical form of content MathML to facilitate math search. The 2007 Extreme Markup Languages conference; 2007 Aug 7-10; Montréal, Canada.
  13. Heck A. "Introduction to MAPLE", 3rd Ed. New York: Springer-Verlag; 1996.
  14. Youssef, A. "Information Search And Retrieval of Mathematics Contents: Issues and Methods", The proceeding of the ISCA 14th International Conference on Intelligent and Adaptive Sys- tems and Software Engineering (IASSE-2005), July 20-22,2005, Toronto, Canada.
  15. Thomas W. Parsons, "Introduction to Compiler Construction", Computer Science Press, W. H. Freeman and Company, 1992.
  16. Christopher W. Fraser, Robert R. Henry, Todd A. Proebsting, "BURG -- Fast Optimal Instruction Selection and Tree Parsing", December 1991.
  17. H. Boley and E. Chang, "Digital ecosystems: Principles and semantics," in Proceedings of the Inaugural IEEE International Conference on Digital Ecosystems and Technologies, 2007, pp. 398–403.
  18. P. Dini, N. Rathbone, M. Vidal, P. Hernandez, P. Ferronato, G. Briscoe, and S. Hendryx, "The digital ecosystems research vision:2010 and beyond," European Commission, Tech. Rep. , 2005.
  19. Java Compiler Compiler, https://javacc. dev. java. net/ [accessed, September 2011]
  20. Lozier, D. W. , Miller, B. R. , and Saunders, B. V. , " Design of a Digital Mathematical Library for Science, Technology and Education". Proceeding of the IEEE Forum on Research and Technology Advances in Digital Libraries; IEEE ADL '99, Bal- timore, Maryland, May 1999.
Index Terms

Computer Science
Information Sciences

Keywords

Math Search Expression's Equivalent Forms Mathematical Expression Detecting Equivalency Grammar Text-based Search Systems