(Word Problem) You are to design a Mealy state diagram for a digital lock. Assume that two debounced push-buttons, A and B, are available to enter the combination. An electromechanical interlock guarantees that the buttons cannot be activated simultaneously. The lock should have the following features:

(a) The combination is A-A-B-A-B-A. If this sequence is correctly entered, an output signal is asserted that causes the lock to open.

(b) For any state, three B pulses in a row should guarantee to reset the control to its initial state.

(c) When any out-of-sequence use of the A push-button occurs, an output is asserted that rings a bell to warn that the lock is being tampered with.

Once the lock is open, pressing either A or B will cause the lock to close without signaling an error. Draw a Mealy state diagram for this finite state machine. Indicate what each state represents and what input conditions cause state and output changes. Not everything may have been specified, so write down any assumptions you make.