For each of the following decision problem$1$ P:

i$.$ Describe a way to represent the inputs as strings$($the alphabet doesn$$t have to be binary$).$

ii$.$ Describe a regular expression that represents the language L :$=\{$w $|$ P$($w$)=1\}$ and briefly explain why the regular expression is correct.

Note : You don$$t have to provide the exact regular expression for part $($ii$).$ Describing how you would formulate the regular expression is sufficient, given that the exact regular expression could indeed be obtained by following your solution.

a Input : A binary number

Output : TRUE if the input is divisible by $4,$ FALSE otherwise

b Input : A complete and valid tic$-$tac$-$toe board filled with O and X Output : TRUE if the winner is O$,$ FALSE otherwise