Avoidable Sets and Well Quasi-Orders

Let I be a finite set of words and $\Rightarrow_{I}^{*}$ be the derivation relation generated by the set of productions {e → u | u ∈ I }. Let LIe be the set of words u such that $\epsilon {\Rightarrow_{I}^{*}}$. We prove that the set I is unavoidable if and only if the relation $\Rightarrow_{I}^{*}$ is a well quasi-order on the set LIe. This result generalizes a theorem of [7]. Further generalizations are investigated.

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