Exploring Tetris as a Transformation Semigroup

Tetris is a popular puzzle video game, invented in 1984. We formulate two versions of the game as transformation semigroup and use this formulation to view through lens Krohn-Rhodes theory. In variation upon which it restarts if player loses, we find permutation group structures, including symmetric \(S_5\) contains non-abelian simple subgroup. This implies, at least case, that iterated finitarily computationally universal.