Regular Construction

$($a$)$ Give a regular expression for the language A over $=\{a,b,c\}.$

$A=\{win{}^{**}$: the number $ofc\text{'}sinwis$ divisible $by3,$ and each $c$ has $ab$ directly before $it\}$

$($b$)$ Give the state diagram for an NFA which decides the language $B$ over $=\{0,1\}.$

Make sure to clearly indicate your start state and final state$($s$).$

$B=(1(01{)}^{**}0)0$

NFA to RegEx Conversion

Give a regular expression for the language decided by the following NFA M $.$ Let $=\{0,1\}.$

Show the intermediate GNFAs after removing each state.

More than Regular $[1.$

Using the pumping lemma, prove that the following language $L$ is not regular, $=\{0,1\}.$

$L=\{win{}^{**}$:$w$ has more $1\text{'}s$ than $0\text{'}s\}$