Rule-Based Production of Mathematical Expressions

There are situations in which one needs to write various kinds of mathematical expressions, such as practicing tests and school exams. There is a variety of methods to produce such expressions, but they are usually based on a database. This paper addresses the production of new expressions using the template ones that can be derived from the evaluation process or entered by users. With special limitations on the values of parameters, some templates can be dynamically constructed for the automatic generation of mathematical expressions and represented in the form of classes. For this purpose, a new type of grammar is proposed. This grammar is similar to Context-Free Grammar, but it empowers the producer to gain control over the generation of rules for different expressions. Our work mainly focuses on generating mathematical expressions in a user-oriented way, using a predefined set of templates of production rules. The production of expressions is not completely random, and is based on the defined subject.

[1]  Georgi Smirnov,et al.  Math exercise generation and smart assessment , 2013, 2013 8th Iberian Conference on Information Systems and Technologies (CISTI).

[2]  Amruth N. Kumar,et al.  Explanation of step-by-step execution as feedback for problems on program analysis , and its generation in model-based problem-solving tutors , 2006 .

[3]  José Paulo Leal,et al.  A CLP-Based Tool for Computer Aided Generation and Solving of Maths Exercises , 2003, PADL.

[4]  Michael White,et al.  EXEMPLARS: A Practical, Extensible Framework For Dynamic Text Generation , 1998, INLG.

[5]  Paul Libbrecht,et al.  ActiveMath: A Generic and Adaptive Web-Based Learning Environment , 2001 .

[6]  Frederick J. Newmeyer,et al.  Grammar is Grammar and Usage is Usage , 2003 .

[7]  Tilman Becker,et al.  Practical, Template–Based Natural Language Generation with TAG , 2002, TAG+.

[8]  Holger Stenzhorn XtraGen - A Natural Language Generation System Using XML- and Java-Technologies , 2002, NLPXML@COLING.

[9]  Mir Mohammad Reza Alavi Milani,et al.  A Step-by-Step Solution Methodology for Mathematical Expressions , 2018, Symmetry.

[10]  Susan McRoy,et al.  YAG: A Template-Based Generator for Real-Time Systems , 2000, INLG.

[11]  Daniel Hoffman,et al.  Two case studies in grammar-based test generation , 2010, J. Syst. Softw..

[12]  S. Klai,et al.  Using Maple and the Web to grade mathematics tests , 2000, Proceedings International Workshop on Advanced Learning Technologies. IWALT 2000. Advanced Learning Technology: Design and Development Issues.

[13]  Emiel Krahmer,et al.  Squibs and Discussions: Real versus Template-Based Natural Language Generation: A False Opposition? , 2005, CL.

[14]  Takahide Yoshikawa,et al.  Random program generator for Java JIT compiler test system , 2003, Third International Conference on Quality Software, 2003. Proceedings..

[15]  Emiel Krahmer,et al.  From data to speech: a general approach , 2001, Natural Language Engineering.

[16]  Kevin Knight,et al.  Generation that Exploits Corpus-Based Statistical Knowledge , 1998, ACL.