[4 points] Describe a Turing Machine that accepts { 0

^{n}| n is a power of 2 }. We want a high-level description of this machine in 10 or fewer clear English sentences. Do not give a list of transitions.[4 points] Describe a Turing Machine that, on input a

^{n}, halts with a^{m}on the tape where m = n^{2}. We want a high-level description of this machine in 10 or fewer clear English sentences. Do not give a list of transitions.[6 points] Show that the recursively enumerable languages are closed under

union and

intersection.

[4 points] Show that { a

^{n}b^{n}a^{n}b^{n}a^{n}b^{n}a^{n}b^{n}| n ≥ 1 } can be written as the intersection of two context free languages.