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Journal Articles Theory of Computing Systems Year : 2014

Playing Mastermind with Constant-Size Memory

Abstract

We analyze the classic board game of Mastermind with n holes and a constant number of colors. The classic result of Chvátal (Combinatorica 3:325–329, 1983) states that the codebreaker can find the secret code with Θ(n/logn) 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 Comput. Syst. 39:525–544, 2006) on the memory-restricted black-box complexity of the OneMax function class.

Dates and versions

hal-01086513 , version 1 (24-11-2014)

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Benjamin Doerr, Carola Doerr. Playing Mastermind with Constant-Size Memory. Theory of Computing Systems, 2014, 55, pp.658-684. ⟨10.1007/s00224-012-9438-8⟩. ⟨hal-01086513⟩
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