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\title{\vspace{-3ex}\bf Context-Free Pumping Lemma\\[2ex]
\rm\normalsize CS 311, Fall 2015}
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\paragraph{Exercise 1} Use the context-free pumping lemma to show that the following language is not regular.
\[ \{0^n1^n0^n1^n \;|\; n \geq 0 \} \]

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\paragraph{Exercise 2} Use the context-free pumping lemma to show that the following language is not regular.
\[ \{ a+b=c \;|\; a,b,c \in \{0,1\}^* \text{ and the binary numbers represented by $a$ and $b$ sum to $c$} \} \]

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