English

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

R2 v1 2026-07-01T05:58:37.693Z