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arXiv · 1604.05431

Permutations of context-free, ET0L and indexed languages

Tara Brough·Laura Ciobanu·Murray Elder·Georg Zetzsche
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Abstract

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 Brandst\"adt'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.

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Tara Brough, Laura Ciobanu, Murray Elder, Georg Zetzsche. 2016-04-19. Permutations of context-free, ET0L and indexed languages. https://arxiv.org/abs/1604.05431

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