$($b$)$ Define and draw a finite State Machine $($FSA$)$ M$2$ for the following patterns. Mark

your Start State and Final States clearly.

all strings that have even number of $0$s followed immediately by even number if $1$s$.$

The string may start with anything other than $0$ or $1$ from the alphabet $\{0,1,2,3\}$

$(6$ points$)$

Show that the following strings will be accepted by M$2$: $($by providing the sequence

of states and the type of the end state$)$: $(3$ points$)$

$2001111$

$333322211$

$323200$

$0011$

Show that the following strings will not be accepted by M$2$: $($by providing the

sequence of states and the type of the end state$)$: $(3$ points$)$

$20111$

$33320101$

$($See below$).$

You are allowed to simplify problem $2($b$)$ to mean that the string may or may not start

with $2$ or $3.$ And even number of zeros are followed by even number of $1$s$.$ There is no

digit $2$ or $3$ in the middle of the string. If you like you may use the empty string symbol

$$

as an empty character for a transition that has no character from one state to another

state.