Permutation closure for multiple context-free languages
Formal Languages and Automata Theory
2025-09-29 v1 Group Theory
Abstract
We prove that the \emph{permutation closure} of a multiple context-free language is multiple context-free, which extends work of Okhotin and Sorokin [LATA 2020] who showed closure under \emph{cyclic shift}, and complements work of Brandst\"adt [1981, RAIRO Inform. Th\'{e}or.] (resp. Brough \emph{et al.} [2016, Discrete Math. Theor. Comput. Sci.]) who showed the same result for regular, context-sensitive, recursively enumerable (resp. EDT0L and ET0L) languages. In contrast to Okhotin and Sorokin who work with grammars, our proof uses restricted tree stack automata due to Denkinger [DLT 2016].
Cite
@article{arxiv.2509.22239,
title = {Permutation closure for multiple context-free languages},
author = {Andrew Duncan and Murray Elder and Lisa Frenkel and Mengfan Lyu},
journal= {arXiv preprint arXiv:2509.22239},
year = {2025}
}
Comments
20 pages, 5 figures