License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2012.441
URN: urn:nbn:de:0030-drops-34112
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3411/
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Doerr, Benjamin ; Winzen, Carola

Playing Mastermind With Constant-Size Memory

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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.

BibTeX - Entry

@InProceedings{doerr_et_al:LIPIcs:2012:3411,
  author =	{Benjamin Doerr and Carola Winzen},
  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 =	{Christoph D{\"u}rr and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3411},
  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}
}

Keywords: Algorithms, Mastermind, black-box complexity, memory-restricted algorithms, query complexity
Collection: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Issue Date: 2012
Date of publication: 24.02.2012

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