1. **Problem Statement:** Construct a Turing machine (TM) that accepts the language consisting of the single string $w = \text{aabb}$. This means the TM should accept if the input tape contains exactly "aabb" and reject otherwise. 2. **Key Idea:** The TM will read the input from left to right, verifying each character matches the expected sequence "aabb". If the input matches exactly, the TM enters an accept state; otherwise, it rejects. 3. **States and Transitions:** - Start at state $q_0$. - Read 'a' at $q_0$, move right to $q_1$. - At $q_1$, read 'a', move right to $q_2$. - At $q_2$, read 'b', move right to $q_3$. - At $q_3$, read 'b', move right to $q_4$. - At $q_4$, check for blank symbol (end of input). If blank, accept; else reject. 4. **Formal Description:** - $\delta(q_0, a) = (q_1, a, R)$ - $\delta(q_1, a) = (q_2, a, R)$ - $\delta(q_2, b) = (q_3, b, R)$ - $\delta(q_3, b) = (q_4, b, R)$ - $\delta(q_4, \sqcup) = (q_{accept}, \sqcup, R)$ - Any other input at any state leads to $q_{reject}$. 5. **Explanation:** The TM reads each character in sequence, ensuring the input matches "aabb" exactly. If any character differs or the input is longer or shorter, the TM rejects. 6. **Final Answer:** The TM accepts the language $\{\text{aabb}\}$ by following the above transitions and states.