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arXiv · 2004.09022

Exploring Tetris as a Transformation Semigroup

Peter C. Jentsch·Chrystopher L. Nehaniv
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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 $S_5$ 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.

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BibTeXRIS

Peter C. Jentsch, Chrystopher L. Nehaniv. 2020-04-20. Exploring Tetris as a Transformation Semigroup. https://arxiv.org/abs/2004.09022

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