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.

Read more about this topic:  Context-free Language

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