$2$: NFA

$($a$)(3$pts$)$ Construct an NFA that accepts binary strings over alphabet $\{x,y\}$ that have $y$ as the

second$-$to$-$last symbol.

$($b$)(8$pts$)$ Give the state diagrams of NFAs with the specified number of states recognizing each

of the following languages. The alphabet is $\{x,y\}.$

contains the substring $xyxy(5$ states or less$)$

$L_9=\{\begin{array}{c}w|w\end{array}$ contains an even number of $x^{\text{'}}s$ or contains exactly two $\{$:$y^{\text{'}}s\}(6$ states or less$)$

$($c$)(7$pts$)$ Convert the following NFA to a DFA. The alphabet is $\{0,1\}.$ Show your work for full

credit.