Context-free Language - Closure Properties

Closure Properties

Context-free languages are closed under the following operations. That is, if L and P are context-free languages, the following languages are context-free as well:

• the union of L and P
• the reversal of L
• the concatenation of L and P
• the Kleene star of L
• the image of L under a homomorphism
• the image of L under an inverse homomorphism
• the cyclic shift of L (the language )

Context-free languages are not closed under complement, intersection, or difference. However, if L is a context-free language and D is a regular language then both their intersection and their difference are context-free languages.