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Well quasi-orders, unavoidable sets, and derivation systems

Published online by Cambridge University Press:  18 October 2006

Flavio D'Alessandro  and
Stefano Varricchio
Flavio D'Alessandro
Affiliation:
Dipartimento di Matematica, Università di Roma “La Sapienza” Piazzale Aldo Moro 2, 00185 Roma, Italy; [email protected]
Stefano Varricchio
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica, 00133 Roma, Italy; [email protected]
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Abstract

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.

Keywords

Well quasi-orderscontext-free languages.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 3: Word Avoidability Complexity And Morphisms (WACAM) , July 2006 , pp. 407 - 426
Copyright
© EDP Sciences, 2006

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