$1-$a$)$ Describe a deterministic Turing Machine M that accepts inputs of $0$s and $1$s in which

the number of $1$s is divisible by $3$ and the number of $0$s is a even number $($hint find first a

corresponding DFA$).$ The tape symbols are $\backslash$Gamma $=\{0,1,$b$\},$ and the alphabet is $=\{0,1\}$ and the

original state is q$0$ and the halting states are qy and qn$.$

$1-$b$)$ What is T$($n$)($time complexity$)$ for the Turing machine in question $1$a$,$ and for inputs of size n$.$ Is

the language L accepted by M in P $($polynomial time deterministic Turing machine$)?1-$b$)$ What is $T(n)($time complexity$)$ for the Turing machine in question $1$a$,$ and for inputs of size $n.$ Is

the language L accepted by M in $P($polynomial time deterministic Turing machine$)?$