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DOI: 10.4230/LIPIcs.STACS.2012.441

Playing Mastermind With Constant-Size Memory

Authors: Benjamin Doerr and Carola Winzen

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Abstract

We analyze the classic board game of Mastermind with n holes and a constant number of colors. The classic result of Chvatal (Combinatorica 3 (1983), 325-329) states that the codebreaker can find the secret code with Theta(n / log n) questions. We show that this bound remains valid if the codebreaker may only store a constant number of guesses and answers. In addition to an intrinsic interest in this question, our result also disproves a conjecture of Droste, Jansen, and Wegener (Theory of Computing Systems 39 (2006), 525-544) on the memory-restricted black-box complexity of the OneMax function class.

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Benjamin Doerr and Carola Winzen. Playing Mastermind With Constant-Size Memory. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 441-452, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{doerr_et_al:LIPIcs.STACS.2012.441,
  author =	{Doerr, Benjamin and Winzen, Carola},
  title =	{{Playing Mastermind With Constant-Size Memory}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{441--452},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.441},
  URN =		{urn:nbn:de:0030-drops-34112},
  doi =		{10.4230/LIPIcs.STACS.2012.441},
  annote =	{Keywords: Algorithms, Mastermind, black-box complexity, memory-restricted algorithms, query complexity}
}

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Playing Mastermind With Constant-Size Memory

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