Well quasi-orders, unavoidable sets, and derivation systems

D'Alessandro, Flavio; Varricchio, Stefano

doi:10.1051/ita:2006019

D'Alessandro, Flavio ; Varricchio, Stefano

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 407-426.

Résumé

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

Zbl

DOI : 10.1051/ita:2006019

Classification : 68Q45, 68R15
Mots clés : well quasi-orders, context-free languages

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     title = {Well quasi-orders, unavoidable sets, and derivation systems},
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     pages = {407--426},
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D'Alessandro, Flavio; Varricchio, Stefano. Well quasi-orders, unavoidable sets, and derivation systems. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 407-426. doi : 10.1051/ita:2006019. http://www.numdam.org/articles/10.1051/ita:2006019/

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