| 1. | There exists a Pumping lemma for context-free languages.
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| 2. | The proof of the pumping lemma is actually pretty simple.
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| 3. | :I'm guessing you mean the pumping lemma for regular languages.
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| 4. | As there are no strings of this length the pumping lemma is not violated.
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| 5. | To prove that a given language is not context-free, one may employ the pumping lemma for context-free languages
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| 6. | By the pumping lemma, there exists an integer " p " which is the pumping length of language " L ".
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| 7. | Finite languages trivially satisfy the pumping lemma by having " p " equal to the maximum string length in " L " plus one.
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| 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 ".
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| 9. | This process of " pumping up " additional copies of " v " and " x " is what gives the pumping lemma its name.
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| 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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