On Total Regulators Generated by Derivation Relations

A derivation relation is a total regulator on Σ* if for every language L\(\subseteq\) Σ*, the set of all words derivable from L is a regular language. We show that for a wide class of derivation relations \(= \mathop = \limits_P^* > , = \mathop = \limits_P^* > \) 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 (OS) derivation relations which are total regulators.

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