THE LIT-ONLY σ-GAME: SOME MATHEMATICS BEHIND A PUZZLE FOR KIDS

The lit-only σ-game is a nondeterministic linear dynamical process whose local transition rule is specified by a digraph. The player of the game can choose among several possible transitions at each step and aim to achieve certain global phase transition. This essay tries to popularize this game to kids for their fun. We also give readers a taste for some possible mathematics behind the game. The paper basically contains no proofs and many ideas are not presented in their full details. We invite the readers to venture out into the world of the lit-only σ-game and other discrete-time graph processes.