SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Antirandomizing the Wrong Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Theoretical Computer Science
Theoretical Computer Science - Algorithmic combinatorial game theory
The Guessing Secrets problem: a probabilistic approach
Journal of Algorithms
Guessing secrets efficiently via list decoding
ACM Transactions on Algorithms (TALG)
Two cooperative versions of the Guessing Secrets problem
Information Sciences: an International Journal
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Suppose we are given some fixed (but unknown) subset X of a set Ω = F2n, where F2 denotes the field of two elements. We would like to learn as much as possible about the elements X by asking certain binary questions. Each "question" Q is some element of Ω, and the "answer" to Q is just the inner product Q·x (in F2) for some x ε X. However, the choice of x is made by a truthful (but possibly malevolent) adversary A, whom we may assume is trying to choose answers so as to as yield as little information as possible about X. In this paper, we study various aspects of this problem. In particular, we are interested in extracting as much information as possible about X from A's answers. Although A can prevent us from learning the identity of any particular element of X, with appropriate questions we can still learn a lot about X. We determine the maximum amount of information that can be recovered and discuss the optimal strategies for selecting questions. For the case that |X| = 2, we give an O(n3) algorithm for an optimal strategy. However, for the case that |X| ≥ 3, we show that no such polynomial-time algorithm can exist, unless P = NP.