Do you really mean what you actually enforced? Edit Automata revisited

In the landmark paper on the theoretical side of Polymer, Ligatti and his co-authors have identied a new class of enforcement mechanisms based on the notion of edit automata, that can transform sequences and enforce more than simple safety properties. We show that there is a gap between the edit automata that one can possibly write (e.g. by Ligatti et al in their running example) and the edit automata that are actually constructed according the theorems from Ligatti's IJIS paper and IC follow-up paper by Talhi et al. Ligatti's automata" are just a particular kind of edit automata. Thus