Solving General Arithmetic Word Problems

This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional annotations or predefined templates. We develop a theory for expression trees that can be used to represent and evaluate the target arithmetic expressions; we use it to uniquely decompose the target arithmetic problem to multiple classification problems; we then compose an expression tree, combining these with world knowledge through a constrained inference framework. Our classifiers gain from the use of {\em quantity schemas} that supports better extraction of features. Experimental results show that our method outperforms existing systems, achieving state of the art performance on benchmark datasets of arithmetic word problems.Comment: EMNLP 201

Solving Commutative Relaxations of Word Problems

We present an algebraic characterization of the standard commutative relaxation of the word problem in terms of a polynomial equality. We then consider a variant of the commutative word problem, referred to as the “Zero-to-All reachability” problem. We show that this problem is equivalent to a finite number of commutative word problems, and we use this insight to derive necessary conditions for Zero-to-All reachability. We conclude with a set of illustrative examples

Solving moment problems by dimensional extension

The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of positive functionals on certain spaces of rational functions developed in the first part, for decomposing a polynomial which is positive on such a semi-algebraic set into a canonical sum of squares of rational functions times explicit multipliers.Comment: 21 pages, published version, abstract added in migratio

Solving XCSP problems by using Gecode

Gecode is one of the most efficient libraries that can be used for constraint solving. However, using it requires dealing with C++ programming details. On the other hand several formats for representing constraint networks have been proposed. Among them, XCSP has been proposed as a format based on XML which allows us to represent constraints defined either extensionally or intensionally, permits global constraints and has been the standard format of the international competition of constraint satisfaction problems solvers. In this paper we present a plug-in for solving problems specified in XCSP by exploiting the Gecode solver. This is done by dynamically translating constraints into Gecode library calls, thus avoiding the need to interact with C++.Comment: 5 pages, http://ceur-ws.org/Vol-810 CILC 201

Solving Problems with the Percentage Bar

At the end of primary school all children more of less know what a percentage is, but yet they often struggle with percentage problems. This article describes a study in which students of 13 and 14 years old were given a written test with percentage problems and a week later were interviewed about the way they solved some of these problems. In a teaching experiment the students were then taught the use of the percentage bar. Although the teaching experiment was very short - just one lesson - the results confirm that the percentage bar is a powerful model that deserves a central place in the teaching of percentages