Permutation closure for multiple context-free languages
Abstract
We prove that the 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 cyclic shift, and complements work of Brandst\"adt [1981, RAIRO Inform. Th\'eor.] (resp. Brough 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].
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.