A traffic light is installed at a junction of a railroad and a road. The light is controlled by two switches in the rails placed 1 mile apart on either side of the junction. A switch is turned on when the train is over it and is turned off otherwise. The traffic light changes from green (logic 0) to red (logic 1) when the beginning of the train is 1 mile from the junction. The light changes back to green when the end of the train is 1 mile away from the junction. Assume that the length of the train is less than 2 miles.

(a) Obtain a primitive flow table for the circuit.

(b) Show that the flow table can be reduced to four rows.