Playing Mastermind With Constant-Size Memory

Doerr, Benjamin; Winzen, Carola

doi:10.4230/LIPIcs.STACS.2012.441

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Playing Mastermind With Constant-Size Memory

Authors Benjamin Doerr, Carola Winzen

Part of: Volume: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2012-02-24

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LIPIcs.STACS.2012.441.pdf

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Document Identifiers

DOI: 10.4230/LIPIcs.STACS.2012.441
URN: urn:nbn:de:0030-drops-34112

Subject Classification

Keywords

Algorithms
Mastermind
black-box complexity
memory-restricted algorithms
query complexity

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.STACS.2012.441

Author Details

Benjamin Doerr

Carola Winzen

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