Recreational Formal Methods: Designing Vacuum Cleaning Trajectories

We study an example due to Wooldridge of a small robotic agent that will vacuum clean a room. The room is an n × n grid and at any point the robot can move forward one step or turn right 90 degrees. The problem is to find a deterministic strategy for the robot in which (1) its next action only depends on its current square and orientation (one of north, west, south, east), and (2) all squares are visited infinitely often. We use a model checker and a SAT solver to find such strategies, and a proof assistant to exhibit certain symmetries in the problem.