Consider a 10x10 grid without any obstacles, and a robot with the same specification as our boundary following robot: eight sensors and four actions.

1. Design a reactive production system to control the robot to go to one of the four corners, wherever its initial position is.2

2. Show that it is not possible to have a reactive production system to make the robot visit every cell in the grid.

3. Design a state machine to achieve the above task. In addition to having memory about previous action taken and previous sensory input, you can have internal variables (mental states) and actions to change the values of these variables.