2 citations · 4 across the 6 of their papers we have counts for
6 papers
Languages, groups and equations
Laura Ciobanu, Alex Levine
The survey provides an overview of the work done in the last 10 years to characterise solutions to equations in groups in terms of formal languages. We begin with the work of Cioba…
Post's correspondence problem for hyperbolic and virtually nilpotent groups
Laura Ciobanu, Alex Levine, Alan D. Logan
Post's Correspondence Problem (the PCP) is a classical decision problem in theoretical computer science that asks whether for pairs of free monoid morphisms t…
Quadratic Diophantine equations, the Heisenberg group and formal languages
Alex Levine
We express the solutions to quadratic equations with two variables in the ring of integers using EDT0L languages. We use this to show that EDT0L languages can be used to describe t…
EDT0L solutions to equations in group extensions
Alex Levine
We show that the class of groups where EDT0L languages can be used to describe solution sets to systems of equations is closed under direct products, wreath products with finite gr…
Equations in virtually class 2 nilpotent groups
Alex Levine
We give an algorithm that decides whether a single equation in a group that is virtually a class nilpotent group with a virtually cyclic commutator subgroup, such as the Heisen…
Equations in virtually abelian groups: languages and growth
Alex Evetts, Alex Levine
This paper explores the nature of the solution sets of systems of equations in virtually abelian groups. We view this question from two angles. From a formal language perspective,…