Pushdown Automaton: CFL and the pumping lemma

Usage of the lemma - Example
• We use the pumping lemma to prove that the
language L={a n b n c n |n0} is not context-free.
Proof:
• Assume, by contradiction, that L is context-free
thus satisfying the lemma.
• Let p be the pumping length for L.
• We select the string w= a p b p c p . wL and |w|>p,
so it can be pumped.
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