Editing Context-sensitive grammar (section)

=== Closure properties ===
Context-sensitive languages are closed under [[complement (set theory)|complement]]. This 1988 result is known as the [[Immerman–Szelepcsényi theorem]].<ref name="flac"/>
Moreover, they are closed under [[union (set theory)|union]], [[intersection (set theory)|intersection]], [[concatenation#Concatenation of sets of strings|concatenation]], [[String substitution|substitution]],<ref group=note>more formally: if ''L'' ⊆ Σ<sup>*</sup> is a context-sensitive language and ''f'' maps each ''a''∈Σ to a context-sensitive language ''f''(''a''), the ''f''(''L'') is again a context-sensitive language</ref> [[inverse string homomorphism|inverse homomorphism]], and [[Kleene plus]].<ref>(Hopcroft, Ullman, 1979); Exercise S9.10, p.&nbsp;230–231</ref>

Every [[recursively enumerable language]] ''L'' can be written as ''h''(''L'') for some context-sensitive language ''L'' and some [[string homomorphism]] ''h''.<ref>(Hopcroft, Ullman, 1979); Exercise S9.14, p.&nbsp;230–232. ''h'' maps each symbol to itself or to the empty string.</ref>