论文标题
邪恶吊手的计算复杂性
The Computational Complexity of Evil Hangman
论文作者
论文摘要
Hangman的游戏是一款古典不对称的两个玩家游戏，其中一个玩家（Setter）从一种语言中选择一个秘密单词，另一个玩家，猜测者试图通过单字匹配的查询来发现，并通过本字母的所有出现（如果有）来回答。在《邪恶的吊手变体》中，设置者可以在游戏中更改秘密单词，只要新选择与已经给出的猜测者的信息一致。我们表明，邪恶吊手的贪婪策略可以任意地表现远非最佳，最重要的是，作为一个邪恶的吊手式设置者，最佳的比赛在计算上很困难。后者的结果甚至可以使对语言的完美知识，对于几类语言，从有限到图灵可计算。这些证明是基于在3个规范图和成员资格问题上的主导设置的减少基础上，该组合问题已知在计算上已经很难。
The game of Hangman is a classical asymmetric two player game in which one player, the setter, chooses a secret word from a language, that the other player, the guesser, tries to discover through single letter matching queries, answered by all occurrences of this letter if any. In the Evil Hangman variant, the setter can change the secret word during the game, as long as the new choice is consistent with the information already given to the guesser. We show that a greedy strategy for Evil Hangman can perform arbitrarily far from optimal, and most importantly, that playing optimally as an Evil Hangman setter is computationally difficult. The latter result holds even assuming perfect knowledge of the language, for several classes of languages, ranging from Finite to Turing Computable. The proofs are based on reductions to Dominating Set on 3-regular graphs and to the Membership problem, combinatorial problems already known to be computationally hard.
