1. There exists a Pumping lemma for context-free languages. 2. The proof of the pumping lemma is actually pretty simple. 3. :I'm guessing you mean the pumping lemma for regular languages. 4. As there are no strings of this length the pumping lemma is not violated. 5. To prove that a given language is not context-free, one may employ the pumping lemma for context-free languages 6. By the pumping lemma , there exists an integer " p " which is the pumping length of language " L ". 7. Finite languages trivially satisfy the pumping lemma by having " p " equal to the maximum string length in " L " plus one. 8. The language can easily be shown to be neither context free by applying the respective pumping lemmas for each of the language classes to " L ". 9. This process of " pumping up " additional copies of " v " and " x " is what gives the pumping lemma its name. 10. This grammar generates the language \ { a ^ n b ^ n : n \ ge 1 \ }, which is not regular ( according to the pumping lemma for regular languages ). 
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