For the second and fourth symmetrical example. However, if a language is is not context-free, use proof by contradiction and the pumping. Share on Facebook Share. If a language is not pumpable, then it is not.
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Clearly this is not in the language. Context-free languages and context-free grammars have applications in computer science and linguistics such as natural language processing and computer language design. For example, there is a regular language that can generate all strings that have an even number of zeroes, but there is not a regular language that can generate all strings that have an equal number of ones and zeroes � a context-free language can do this, however. If CFL's were closed under intersection then there would be CFLs that violate the pumping lemma for context-free languages see the next section for more details which cannot be.
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