图灵完备性与席德·梅尔的文明
Turing Completeness and Sid Meier's Civilization
AI总结：
本文通过在Sid Meier's Civilization系列三款游戏中构建通用图灵机，证明其具有图灵完备性，并展示了三状态Busy Beaver算法的示例执行。
摘要：
我们证明了席德·梅尔的文明系列的三款策略电子游戏：Sid Meier's Civilization: Beyond Earth、Sid Meier's Civilization V和Sid Meier's Civilization VI是图灵完备的。我们通过为每款游戏构建一个通用图灵机来实现这一点，仅使用游戏中存在的元素，并将其内部规则和机制作为转移函数。此类机器的存在意味着在所作假设下，这些游戏是不可判定的。我们展示了在运行的游戏会话中这些机器的构造，并提供了算法——三状态Busy Beaver——在其中一台机器上的示例执行。
英文摘要：
We prove that three strategy video games from the Sid Meier's Civilization series: Sid Meier's Civilization: Beyond Earth, Sid Meier's Civilization V, and Sid Meier's Civilization VI, are Turing complete. We achieve this by building three universal Turing machines-one for each game-using only the elements present in the games, and using their internal rules and mechanics as the transition function. The existence of such machines imply that under the assumptions made, the games are undecidable. We show constructions of these machines within a running game session, and we provide a sample execution of an algorithm-the three-state Busy Beaver-with one of our machines.
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