License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2021.23
URN: urn:nbn:de:0030-drops-127840
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12784/
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Barbay, Jérémy ; Subercaseaux, Bernardo

The Computational Complexity of Evil Hangman

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LIPIcs-FUN-2021-23.pdf (0.6 MB)


Abstract

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.

BibTeX - Entry

@InProceedings{barbay_et_al:LIPIcs:2020:12784,
  author =	{J{\'e}r{\'e}my Barbay and Bernardo Subercaseaux},
  title =	{{The Computational Complexity of Evil Hangman}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{23:1--23:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Martin Farach-Colton and Giuseppe Prencipe and Ryuhei Uehara},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12784},
  URN =		{urn:nbn:de:0030-drops-127840},
  doi =		{10.4230/LIPIcs.FUN.2021.23},
  annote =	{Keywords: combinatorial game theory, computational complexity, decidability, hangman}
}

Keywords: combinatorial game theory, computational complexity, decidability, hangman
Collection: 10th International Conference on Fun with Algorithms (FUN 2021)
Issue Date: 2020
Date of publication: 16.09.2020


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