Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for higher-order mathematics skills including word problems. Research indicates equal-sign instruction can alter how typically-developing students use the equal sign, but no study ...

Abstract For quadratic word equations, there exists an algorithm based on rewriting rules which generates a directed graph describing all solutions to the equation. regular equations – those for each variable occurs at most once side of equation we investigate properties this graph, such as bounds its diameter, size, and DAG-width, well providing some insights into symmetries in structure. As c...

Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justified at all. However, a linear Diophantine equation can be viewed as a special case of a system of wo...

Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that turns this equation into true equality of strings. The computational complexity of this problem remains unknown, with the best lower and upper bounds being, re...

Ehrenfeucht's Conjecture is equivalent with the ascending chain condition for word equations. A related conjecture concerns the descending chain condition for word equations. We show that if this conjecture holds then an arbitrary in nite language L possesses a nite subset F such that the language L F is a disjoint union of its nite test sets. We prove this consequence of the descending chain c...

Context uniication is a natural variant of second order uniica-tion that represents a generalization of word uniication at the same time. While second order uniication is wellknown to be undecidable and word uniication is decidable it is currently open if solvability of context equations is decidable. We show that solvability of systems of context equations with two context variables is decidab...

We present version 1.0 of the Norn SMT solver for string constraints. Norn is a solver for an expressive constraint language, including word equations, length constraints, and regular membership queries. As a feature distinguishing Norn from other SMT solvers, Norn is a decision procedure under the assumption of a set of acyclicity conditions on word equations, without any restrictions on the u...

Decidability of non-structural subtype entailment is a long-standing open problem in programming language theory. In this paper, we apply automata theoretic methods to characterize the problem equivalently by using regular expressions and word equations. This characterization induces new results on non-structural subtype entailment, constitutes a promising starting point for further investigati...

We present an approach for automatically learning to solve algebra word problems. Our algorithm reasons across sentence boundaries to construct and solve a system of linear equations, while simultaneously recovering an alignment of the variables and numbers in these equations to the problem text. The learning algorithm uses varied supervision, including either full equations or just the final a...