Formal languages, quadratic Diophantine equations and the Heisenberg group

Abstract

We show that EDT0L languages can be used to describe the solutions to one-variable equations in the Heisenberg group. To do this, we first express the solutions to quadratic equations with two variables in the ring of integers using EDT0L languages, and then we reduce the question of solving a one-variable equation in the Heisenberg group to solving an equation in the ring of integers.

Multiplication tables and word-hyperbolicity in free products of semigroups, monoids, and groups

“…especially [33], see also [75,98,25]). The research topic remains very active; particularly the connections between ET0L and EDT0L languages and equations over groups and monoids have flourished in recent years [48,30,33,31,37,32,83,47,84,77]. There are also recent links with geometric group theory.…”