$[10$ pts$.]$

$9.$ Consider the finite state automaton $A,$ given by the transition diagram shown, has a next$-$state function $N$ and an eventual state function $N^{**}$

$($a$)$ Find $N^{**}(s_1,1100110101)$

$($b$)$ Find $N(s_3,1)$ and Find $N(s_1,0)$

$($c$)$ What is the language accepted by the automaton?