please help me solve problem number 1.

Probleml: Consider the finite state machine shown below. I PS A x=0 C, 10 D. 01 A, 01 C, 10 B, 10 C, 10 A, 10 D.10 D Next state, output (5pts.) Determine, if possible, an input sequence Xl that would take this machine from state A to state D. (5pts.) b. Determine, if possible, an input sequence X2 that, when applied to this machine, will take this machine into the state C regardless of the initial state of this machine. (Ignore the outputs) (5pts.) c. Determine, if possible, an input sequence X3 that, when applied to the machine and after observing the outputs, will allow you to determine the initial state of the machine. (20pts.) d. Try to put all these concepts together to develop a methodology for testing finite state machines. What other concepts, if any, do you need that have not been discussed above to solve this problem? (Limit yourself to only 30 minutes for this problem)