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Michael Sipser Edition 3 Exercise 5 Question 22 (Page No. 240)
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Show that $A$ is Turing-recognizable iff $A \leq_{m} A_{TM}$.
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Michael Sipser Edition 3 Exercise 5 Question 7 (Page No. 239)
Show that if $A$ is Turing-recognizable and $A\leq_{m} \overline{A},$ then $A$ is decidable.
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Michael Sipser Edition 3 Exercise 5 Question 25 (Page No. 240)
Give an example of an undecidable language $B$, where $B \leq_{m} \overline{B}$.
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Michael Sipser Edition 3 Exercise 5 Question 23 (Page No. 240)
Show that $A$ is decidable iff $A \leq_{m} 0 ^{\ast} 1^{\ast}$ .
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Michael Sipser Edition 3 Exercise 5 Question 21 (Page No. 240)
Let $AMBIG_{CFG} = \{\langle G \rangle \mid \text{G is an ambiguous CFG}\}$. Show that $AMBIG_{CFG}$ is undecidable. (Hint: Use a reduction from $PCP$ ... $a_{1},\dots,a_{k}$ are new terminal symbols. Prove that this reduction works.)
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