arXiv subjects

Lisa Frenkel

Publications and source records attributed to Lisa Frenkel.

2 recordsLinked to original sources

arXiv2025

Permutation closure for multiple context-free languages

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].

cs.FL↗

arXiv2025

A substitution lemma for multiple context-free languages

We present a necessary condition for an infinite language to be multiple context-free, which we call a Substitution Lemma. We apply it to show a sample selection of languages are not multiple context-free, including the word problem of the group $F_2\times F_2$. We also show that groups with multiple context-free word problem have decidable rational subset membership problem. Our result contrasts with previous work showing that the standard pumping lemma for context-free languages cannot be generalised to multiple context-free languages, and that weak variants of generalised Ogden's lemma do not apply to multiple context-free languages.

cs.FL↗