On Total Regulators Generated by Derivation Relations

Abstract A derivation relation is a total regulator on Σ ∗ if, for every language L ⊆ Σ ∗ , the set of all words derivable from L is a regular language. We show that for a wide class of derivation relations ⇒ P ∗ , ⇒ P ∗ is a total regulator on Σ ∗ if,and only if it is a well-quasi-order (wqo) on Σ ∗ . Using wqo theory, we give a characterization of all non-erasing pure context-free (0S) derivation relations which are total regulators.