Determine invariance under changes of generating set

Determine whether the complexity classifications established for the Green representative languages of free inverse monoids are invariant under changing the finite generating set.

Background

The paper’s formal-language results are obtained using specified finite generating sets, principally the standard generating set of a free inverse monoid. It remains unresolved whether the resulting classifications—such as regularity, context-freeness, co-context-freeness, and related distinctions—depend on that choice. The authors explicitly identify invariance under a change of generating set as an important question.