Word equations, constraints and formal languages

In this talk I will give an overview of word equations in free monoids and groups that are `free-like’. I will then discuss how one can express the solutions to word equations as EDT0L languages, and touch upon the (un)decidability of solving word equations with a variety of algebraic and combinatorial constraints.

This is based on work with V. Diekert and M. Elder, and very recent results with G. Zetzsche.