Permutations of context-free, ET0L and indexed languages

Tara Brough (1) , Laura Ciobanu (2) , Murray Elder (3) , Georg Zetzsche (4)

1 ULISBOA - Universidade de Lisboa = University of Lisbon
2 UNINE - Université de Neuchâtel = University of Neuchatel
3 UoN - University of Newcastle [Callaghan, Australia]
4 LSV - Laboratoire Spécification et Vérification [Cachan]

For a language $L$, we consider its cyclic closure, and more generally the language $C^{k}(L)$, which consists of all words obtained by partitioning words from $L$ into $k$ factors and permuting them. We prove that the classes of ET0L and EDT0L languages are closed under the operators $C^k$. This both sharpens and generalises Brandstädt's result that if $L$ is context-free then $C^{k}(L)$ is context-sensitive and not context-free in general for $k \geq 3$. We also show that the cyclic closure of an indexed language is indexed.

Mots clés: ET0L; EDT0L; indexed; context-free; cyclic closure

Domaines: Mathématique discrète [cs.DM]

Tara Brough, Laura Ciobanu, Murray Elder, Georg Zetzsche. Permutations of context-free, ET0L and indexed languages. Discrete Mathematics and Theoretical Computer Science, 2016, Vol. 17 no. 3 (3), pp.167-178. ⟨10.46298/dmtcs.2164⟩. ⟨hal-01352858⟩