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.

中文翻译：

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邪恶刽子手的计算复杂性

Hangman 游戏是一种经典的非对称双人游戏，其中一个玩家，即二传手，从一种语言中选择一个秘密词，另一个玩家，即猜测者，试图通过单字母匹配查询来发现，回答所有出现的这个信如果有的话。在 Evil Hangman 变体中，只要新的选择与已经提供给猜测者的信息一致，二传手就可以在游戏过程中更改密语。我们表明，Evil Hangman 的贪婪策略可以任意执行远非最佳，最重要的是，作为 Evil Hangman 设置者以最佳方式进行游戏在计算上是困难的。对于从有限到图灵可计算的几类语言，即使假设对语言有完美的了解，后一个结果也成立。