## Brough, Tara and Ciobanu, Laura and Elder, Murray and Zetzsche, Georg - Permutations of context-free, ET0L and indexed languages

dmtcs:2164 - Discrete Mathematics & Theoretical Computer Science, May 31, 2016, Vol. 17 no. 3
Permutations of context-free, ET0L and indexed languages

Authors: Brough, Tara and Ciobanu, Laura and Elder, Murray and Zetzsche, Georg

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.

Volume: Vol. 17 no. 3
Section: Automata, Logic and Semantics
Published on: May 31, 2016
Submitted on: January 5, 2015
Keywords: cyclic closure, context-free,ET0L, EDT0L, indexed,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]