论文标题
探索俄罗斯方块作为转型半群
Exploring Tetris as a Transformation Semigroup
论文作者
论文摘要
俄罗斯方块是一款流行的拼图视频游戏，于1984年发明。我们将游戏的两个版本作为转换半群，并使用此公式通过Krohn-Rhodes理论的镜头来查看游戏。在播放器丢失的游戏的变体中，我们找到了置换组结构，包括对称组$ s_5 $，其中包含一个非亚伯利亚简单组作为子组。至少在简单的情况下，这意味着迭代的俄罗斯方块在计算上是有限的。
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.
