论文标题
魔术：聚会就像算术一样困难
Magic: the Gathering is as Hard as Arithmetic
论文作者
论文摘要
魔术：聚会是一款关于魔法战斗的流行且著名的纸牌游戏。最近，包括Chatterjee和Ibsen-Jensen（2016）以及Churchill，Biderman和Herrick（2019）在内的几位作者研究了最佳玩魔术的计算复杂性。在本文中，我们表明魔术的``伴侣in- $ n $''问题是$δ^0_n $ - hard，而两人魔术中的最佳游戏通常是非算术的。这些结果适用于如何使用标准大小的比赛法律甲板来实现真正的魔术，并且不依赖随机性或隐藏的信息。我们的论文建立在丘吉尔，Biderman和Herrick（2019）的结构上，以表明这个问题至少与停止问题一样困难。
Magic: the Gathering is a popular and famously complicated card game about magical combat. Recently, several authors including Chatterjee and Ibsen-Jensen (2016) and Churchill, Biderman, and Herrick (2019) have investigated the computational complexity of playing Magic optimally. In this paper we show that the ``mate-in-$n$'' problem for Magic is $Δ^0_n$-hard and that optimal play in two-player Magic is non-arithmetic in general. These results apply to how real Magic is played, can be achieved using standard-size tournament legal decks, and do not rely on stochasticity or hidden information. Our paper builds upon the construction that Churchill, Biderman, and Herrick (2019) used to show that this problem was at least as hard as the halting problem.
