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RAIRO - Theoretical Informatics and Applications (1)

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Well quasi-orders, unavoidable sets, and derivation systems
Flavio D'Alessandro, Stefano Varricchio
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 40 / Issue 3 / July 2006

Published online by Cambridge University Press:

18 October 2006, pp. 407-426

Print publication:

July 2006
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Let I be a finite set of words and $\Rightarrow_I^*$ be the derivation relation generated by the set of productions {ε → u | u ∈ I}. Let $L_I^{\epsilon}$ be the set of words u such that $\epsilon \Rightarrow_I^* u$. We prove that the set I is unavoidable if and only if the relation $\Rightarrow_I^*$ is a well quasi-order on the set $L_I^{\epsilon}$. This result generalizes a theorem of [Ehrenfeucht et al.,Theor. Comput. Sci.27 (1983) 311–332]. Further generalizations are investigated.