Construct a DFA $($by providing its diagram$)$ which accepts the following finite set of strings over

the alphabet $=\{0,1\}$

$\{win{}^{**}||w|=4$ and $w\text{'}s$ two middle symbols $(i.e.,$ the $2nd$ and $3rd)$ are the same $\}$

Present your DFA as a clearly drawn state diagram and explain why the diagram accomplishes

the required task.

In the below problem use the construction from the proof of Theorem $1\mathrm{.}25$ in the textbook

concerning the intersection of regular languages. Namely, design a DFA, A $($by providing its

diagram$),$ which accepts the following language over the alphabet $=\{0,1\}$ :

$L(A)=\{win{}^{**}|$ the number $of{0}^{\text{'}}\text{'}sinwis$ even and the number $of1\text{'}s$ equal $3(mod4)\}$

A should have $$ than $8$ states. It should be clear from your solution how you used the construction

and your diagrams should not have intersecting edges.