A relation-centric algorithm for solving text-diagram function problems

Abstract

A tutorable algorithm for solving text-diagram function (TDF) problems is an essential technology for building the humanoid tutorial service since ”function” is a core portion of mathematics. Solving TDF problems encounters challenges in understanding diagrams, representing the functions of being compound objects, and solving the mixture group of functions and universal relations. To address these challenges, this paper proposes a relation-centric algorithm, leveraging on making breakthrough in handling function, understanding diagram, and generating tutorable solution. The proposed algorithm comprises two phases: problem understanding and symbolic solver. In the problem understanding, it proposes a S2P (Syntax Semantics with Period) model method of acquiring relations from text and a L2 (Line Segment with Labels Pattern) model method of acquiring relations from diagrams. To get the problem fully understood, this phase acquires both universal relations and period relations. In the symbolic solver, the function is first built from the acquired relations. Then an equation-function interaction method is created to solve a mixture system of relations and functions. The developed algorithm is the first one for solving text-diagram function problems. Experimental results show that the proposed algorithm not only has high accuracies of 74.5% on Math23KtoF and 80.8% on TnD1K datasets, but also can produce the tutorable solutions of TDF problems.