Properties of Context-free Languages
- The reverse of a context-free language is context-free, but the complement need not be.
- Every regular language is context-free because it can be described by a context-free grammar.
- The intersection of a context-free language and a regular language is always context-free.
- There exist context-sensitive languages which are not context-free.
- To prove that a given language is not context-free, one may employ the pumping lemma for context-free languages or a number of other methods, such as Ogden's lemma, Parikh's theorem, or using closure properties.
- Context Free Languages are closed under Union, Concatenation, and Kleene star.
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