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Michael Sipser Edition 3 Exercise 2 Question 50 (Page No. 159)
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We defined the $CUT$ of language $A$ to be $CUT(A) = \{yxz| xyz \in A\}$. Show that the class of $CFLs$ is not closed under $CUT$.
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Michael Sipser Edition 3 Exercise 2 Question 53 (Page No. 159)
Show that the class of DCFLs is not closed under the following operations: Union Intersection Concatenation Star Reversal
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Michael Sipser Edition 3 Exercise 2 Question 49 (Page No. 159)
We defined the rotational closure of language $A$ to be $RC(A) = \{yx \mid xy \in A\}$.Show that the class of CFLs is closed under rotational closure.
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Michael Sipser Edition 3 Exercise 2 Question 48 (Page No. 159)
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 $1s$ ... $C_{1}$ is a CFL. Show that $C_{2}$ is not a CFL.
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Michael Sipser Edition 3 Exercise 2 Question 55 (Page No. 159)
Let $G_{1}$ be the following grammar that we introduced in Example $2.45$. Use the DK-test to show that $G_{1}$ is not a DCFG. $R \rightarrow S \mid T$ $S \rightarrow aSb \mid ab$ $T \rightarrow aTbb \mid abb$
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