Let = {0,1}. Let C1 be the language of all strings that

Chapter , Problem 2.48

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QUESTION:

Let \(\Sigma=\{0,1\}\). Let \(C_{1}\) be the language of all strings that contain a 1 in their
middle third. Let \(C_{2}\) be the language of all strings that contain two 1s in their
middle third. So \(C_{1}=\left\{x y z \mid x, z \in \Sigma^{*} \text { and } y \in \Sigma^{*} 1 \Sigma^{*}\right.\), where \(|x|=|z| \geq|y|\}\) and \(C_{2}=\left\{x y z \mid x, z \in \Sigma^{*}\right.\) and \(y \in \Sigma^{*} 1 \Sigma^{*} 1 \Sigma^{*}\), where \(|x|=|z| \geq|y|\}\).

a. Show that \(C_1\) is a CFL.
b. Show that \(C_2\) is not a CFL.

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QUESTION:

Let \(\Sigma=\{0,1\}\). Let \(C_{1}\) be the language of all strings that contain a 1 in their
middle third. Let \(C_{2}\) be the language of all strings that contain two 1s in their
middle third. So \(C_{1}=\left\{x y z \mid x, z \in \Sigma^{*} \text { and } y \in \Sigma^{*} 1 \Sigma^{*}\right.\), where \(|x|=|z| \geq|y|\}\) and \(C_{2}=\left\{x y z \mid x, z \in \Sigma^{*}\right.\) and \(y \in \Sigma^{*} 1 \Sigma^{*} 1 \Sigma^{*}\), where \(|x|=|z| \geq|y|\}\).

a. Show that \(C_1\) is a CFL.
b. Show that \(C_2\) is not a CFL.

ANSWER:

Let = {0,1}. Let C1 be the language of all strings that contain a 1 in their middle third. Let C2 be the la

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