Corpus ID: 226299759

# Mastermind with a Linear Number of Queries

@article{Martinsson2020MastermindWA,
title={Mastermind with a Linear Number of Queries},
author={A. Martinsson and Pascal Su},
journal={ArXiv},
year={2020},
volume={abs/2011.05921}
}
• Published 2020
• Mathematics, Computer Science
• ArXiv
Since the 60's Mastermind has been studied for the combinatorial and information theoretical interest the game has to offer. Many results have been discovered starting with Erdős and Renyi determining the optimal number of queries needed for two colors. For $k$ colors and $n$ positions, Chvatal found asymptotically optimal bounds when $k \le n^{1-\epsilon}$. Following a sequence of gradual improvements for $k \geq n$ colors, the central open question is to resolve the gap between $\Omega(n… Expand 1 Citations #### Figures from this paper Solving Static Permutation Mastermind using$O(n \log n)$Queries • Mathematics • 2021 Permutation Mastermind is a version of the classical mastermind game in which the number of positions n is equal to the number of colors k, and repetition of colors is not allowed, neither in theExpand #### References SHOWING 1-10 OF 19 REFERENCES Playing Mastermind With Many Colors • Mathematics, Computer Science • CTW • 2012 It is shown that an optimal nonadaptive strategy (deterministic or randomized) needs Θ(nlog n) guesses, and if both black and white answer pegs are used, then the O(n log log n) bound holds for up to n2log log n colors. Expand Hardness of Mastermind A proof of the #P-completeness of #MSP under parsimonious reductions is provided, which settles an open problem posed by Stuckman and Zhang in 2005, concerning the complexity of deciding if the secret code is uniquely determined by the previous guesses and responses. Expand The number of pessimistic guesses in Generalized Black-peg Mastermind • Mathematics, Computer Science • Inf. Process. Lett. • 2011 Borders for Generalized Black-peg Mastermind are given for arbitrary numbers p, c and an upper bound recently proved by Goodrich is improved, which is to give bounds for the general case b(p,c). Expand On the algorithmic complexity of the Mastermind game with black-peg results • M. Goodrich • Mathematics, Computer Science • Inf. Process. Lett. • 2009 It is shown that it is NP-complete to determine if a sequence of single- color Mastermind results have a satisfying vector, and how to devise efficient algorithms for discovering a hidden vector through single-color queries. Expand Determination of a subset from certain combinatorial properties • Mathematics • 1966 1. Let N be a finite set of n elements. A collection {Si, S2, . . . , Sm} of subsets of N is called a determining collection if an arbitrary subset T of N is uniquely determined by the cardinalitiesExpand On a Combinatorial Problem in Number Theory 1. Introduction One of the problems mentioned injl] (on p. 187) concerns the estimation of the magnitude of the largest number g(N) such that, from every sequence of N distinct natural numbers, oneExpand The Mastermind Attack on Genomic Data • M. Goodrich • Computer Science • 2009 30th IEEE Symposium on Security and Privacy • 2009 In this paper, we study the degree to which a genomic string,$Q\$,leaks details about itself any time it engages in comparison protocolswith a genomic querier, Bob, even if those protocolsExpand
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• Mathematics, Computer Science
• ArXiv
• 2005
This paper proves that the Mastermind Satisfiability Pro blem (MSP) is NP- complete, and reveals its intrinsic computational property that makes it challenging and interesting. Expand
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It is shown that $$\left\lceil {\frac{m}{n}} \right\rceil$$+ 2nlogn + 2n + 2 queries are sufficient to find any hidden code if m ≥ n. Expand
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The first problem1 which will be discussed in this paper can be formulated as follows: Suppose we are given n coins, which look quite alike, but of which some are false. (For instance suppose thatExpand