Conjunctive languages are closed under inverse homomorphism
نویسنده
چکیده
It is proved that the inverse homomorphic image of every language generated by a conjunctive grammar can be generated by a conjunctive grammar as well, and, given an arbitrary grammar G over an alphabet Γ and a homomorphism h : Σ∗ → Γ∗, a grammar for the language h−1(L(G)) ⊆ Σ∗ can be effectively constructed. Together with the known results on conjunctive grammars, this implies that the language family they generate is a pre-AFL. Résumé On montre que l’image homomorphic inverse de chaque langage produite par une grammaire conjonctive peut être aussi bien produite par une grammaire conjonctive, et, donné une grammaire arbitraire G sur d’un alphabet Γ et un homomorphisme h : Σ∗ → Γ∗, une grammaire pour le langage h−1(L(G)) ⊆ Σ∗ peut être efficacement construit. Avec les résultats connus sur les grammaires conjonctives, ceci implique que la famille de langages qu’elles produisent est une pre-AFL.
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