On total regulators generated by derivation relations (Q1084874)

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