My company has been tasked with building a controller for locking and unlocking a door. Instructions are provided to the controller to govern the state of the door. The instructions are one of L ("lock"), U ("unlock"), or S ("stay"). The controller can be in one of three states: locked, unlocked, or resetting. The controller starts in the locked state. It receives a sequence of L, U, S instructions, and is to respond as follows. If it is locked and receives a L or S, it remains locked. If it is unlocked and receives a U or S, it remains unlocked. If it is locked and receives a U, it becomes unlocked unless the previous instruction (if any) was an L, in which case it becomes resetting. If it is unlocked and receives an L, it becomes locked unless one or both of the two previous instructions (when they exist) was a U, in which case it becomes resetting. When it first becomes resetting, it remains resetting for the next ten instructions and then becomes locked and starts behaving as if it had just commenced operation. (a) Design a DFA with input alphabet {L, U, S} whose states determine the state of the controller in the operation described above. (Your DFA need not have any final states.) (b) Give an English language description of the strings (sequences of instructions) that make the controller locked