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+\begin{solution}{5}
+ \begin{enumerate}
+ \item The intuition would be: for the first $a$ that we read, mark it with $X$ and mark the next $b$ we see with $Y$. Go back to the beginning and repeat. When we read a $Y$ instead of an $a$, we have finished the $a^i$ part of the string, and we can go to a final state. The machine should check that there is a $b$ for every $a$ and that the $a$s and $b$s are consecutive.
+
+ %todo draw machine
+
+ \setcounter{enumi}{2}
+
+ \item The intuition would be: find a $b$ for every $a$, mark both with $X$. Repeat until there are no $a$s left. Then check that there are also no $b$s left.
+
+ %todo draw machine
+ \end{enumerate}
+\end{solution}
+