1. Consider the finite state machine whose next state function and output function are given by: V b 82 $6 85 84 84 86 $1 82 83 84 83 $5 85 82 $3 86 84 $3 and W a b Y N YN Y Y 84 Y Y Y N 85 86 Y Y $1 $2 $3 (a) Apply the minimization process to the above machine as follows: Determine P and provide a brief reason why states are in the same block of the partiton. Determine the remaining partitions in the process being clear at each step to give com- plete information but to not include information that is not needed to make your con- clusion for each comparison of states. Clearly state why you have terminated the process. (b) Let y be a minimal distinguishing string for s4 and 86. Without determining y what is ||y|| and how do you know this? (c) Determine a minimal distinguishing string for 82 and 85. Be sure to give reasons for your answer.. (d) Determine a minimal distinguishing string for s3 and 86. Be sure to give reasons for your answer. (e) Draw the state diagram for the original machine (with starting state ). Your diagram should have no crossing arrows. (f) Draw the state diagram for the minimized machine. Your diagram should have no crossing arrows.