Exploring Tetris as a Transformation Semigroup
Group Theory
2020-04-21 v1 Formal Languages and Automata Theory
Dynamical Systems
Adaptation and Self-Organizing Systems
Abstract
Tetris is a popular puzzle video game, invented in 1984. We formulate two versions of the game as a transformation semigroup and use this formulation to view the game through the lens of Krohn-Rhodes theory. In a variation of the game upon which it restarts if the player loses, we find permutation group structures, including the symmetric group which contains a non-abelian simple group as a subgroup. This implies, at least in a simple case, that iterated Tetris is finitarily computationally universal.
Cite
@article{arxiv.2004.09022,
title = {Exploring Tetris as a Transformation Semigroup},
author = {Peter C. Jentsch and Chrystopher L. Nehaniv},
journal= {arXiv preprint arXiv:2004.09022},
year = {2020}
}