What are the closure properties of context-free languages?

The closure properties of context-free languages refer to the properties that are preserved under certain operations performed on context-free languages. The closure properties of context-free languages are as follows:

1. Union: The union of two context-free languages is also a context-free language. If L1 and L2 are context-free languages, then their union L1 ∪ L2 is also a context-free language.

2. Concatenation: The concatenation of two context-free languages is also a context-free language. If L1 and L2 are context-free languages, then their concatenation L1L2 is also a context-free language.

3. Kleene Star: The Kleene star operation applied to a context-free language results in another context-free language. If L is a context-free language, then L* (Kleene star of L) is also a context-free language.

4. Homomorphism: If a context-free language L is mapped onto another language M by a homomorphism, then M is also a context-free language.

5. Intersection with a Regular Language: The intersection of a context-free language with a regular language is also a context-free language. If L1 is a context-free language and L2 is a regular language, then L1 ∩ L2 is also a context-free language.

6. Reversal: The reversal of a context-free language is also a context-free language. If L is a context-free language, then L^R (reversal of L) is also a context-free language.

These closure properties allow us to perform various operations on context-free languages while ensuring that the resulting language remains context-free.