Word equations, constraints, and formal languages

TL;DR

This paper surveys recent progress on solving word equations with constraints in algebraic structures, emphasizing the significance of formal languages in understanding their properties and solutions.

Contribution

It provides a comprehensive overview of recent developments in word equations with constraints, connecting formal language theory to algebraic problem-solving.

Findings

Formal languages are crucial in analyzing word equations.

Recent advances include new solution techniques for constrained word equations.

The survey highlights open problems and future research directions.

Abstract

In this short survey we describe recent advances on word equations with non-rational constraints in groups and monoids, highlighting the important role that formal languages play in this area.