Probabilistic equivalence verification approach for automatic mathematical solution assessment

Authors:
Minh Luan Nguyen;Siu Cheung Hui;Alvis C. M. Fong
Affiliations:
School of Computer Engineering, Nanyang Technological University, Singapore;School of Computer Engineering, Nanyang Technological University, Singapore;School of Computing and Math Sciences, Auckland University of Technology, New Zealand
Venue:
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Year:
2013

Citing 13
Cited 0

Simple fast algorithms for the editing distance between trees and related problems

SIAM Journal on Computing
Randomized algorithms

ACM Computing Surveys (CSUR)
Pattern matching algorithms

Pattern matching algorithms
Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs

Journal of the ACM (JACM)
Fundamental problems of algorithmic algebra

Fundamental problems of algorithmic algebra
The Debate on Automated Essay Grading

IEEE Intelligent Systems
Computer Algebra and Symbolic Computation: Mathematical Methods

Computer Algebra and Symbolic Computation: Mathematical Methods
Algebraic simplification a guide for the perplexed

SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Modern Computer Algebra

Modern Computer Algebra
Improving Student Performance Using Self-Assessment Tests

IEEE Intelligent Systems
Synthesizing geometry constructions

Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
Learning to grade short answer questions using semantic similarity measures and dependency graph alignments

HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies - Volume 1
In the year of disruptive education

Communications of the ACM

Quantified Score

Hi-index	0.00

Visualization

Abstract

Automatic mathematical solution assessment checks the equivalence of mathematical expressions in the user answer and standard solution. It is a challenging problem as the semantics of mathematical expressions are highly symbolic and equivalent mathematical expressions can be expressed in different forms. In this paper, we propose an effective Probabilistic Equivalence Verification (PEV) approach for automatic mathematical solution assessment. The proposed PEV approach is a randomized method based on the probabilistic numerical equivalence testing of two mathematical expressions. It can avoid false negative errors completely while guaranteeing a small probability of false positive errors to occur. The performance results have shown that the proposed PEV approach has outperformed other popular techniques in Computer Algebra Systems such as Maple and Mathematica.