1. Finite state machine verification [24 points] Specification: A ceiling fan has two pull cords attached to it and one power button that is mounted on the wall by the door to the room. The power button acts as a toggle for activating (and deactivating) the fan - we will call this the "power button". The pull cords control the fan speed and the light bulb The "light cord" activates and deactivates the light bulb on the ceiling fan. The "speed cord" cycles the fan through four speed settings: "1: low speed", "2: medium speed", "3: high speed" and "0: off". When the power button is already on, and the power button is then pressed, all power to the fan is effectively shut off, regardless of whether its light is on or its fan is spinning However, for convenience of use, when the power button is already off, and the power button is then pressed, the power to the fan is resumed in such a way as to make the light bulb turn or and the fan speed is resumed to the speed that it was running prior to shutting off the power button. When first installed, the power button is in the off position (i.e., "unpowered"), and the first time the power button is pressed, the fan speed is "off" and the light-bulb is "on" Finite State Machines: ("pb" stands for "power button", "sc" stands for "speed cord", and "lo stands for "light cord") Fan-Speed Finite State Machine Light Finite State Machine start start fan off, powered fan off, unpower ed light off, unpower ed SC fan off, low low light on speed SC SC lc lc medium speed fan off, medium light off, powered SC high speed fan off, ig