# Three Thresholds for a Liar

@article{Spencer1992ThreeTF, title={Three Thresholds for a Liar}, author={Joel H. Spencer and Peter Winkler}, journal={Combinatorics, Probability and Computing}, year={1992}, volume={1}, pages={81 - 93} }

Motivated by the problem of making correct computations from partly false information, we study a corruption of the classic game “Twenty Questions” in which the player who answers the yes-or-no questions is permitted to lie up to a fixed fraction r of the time. The other player is allowed q arbitrary questions with which to try to determine, with certainty, which of n objects his opponent has in mind; he “wins” if he can always do so, and “wins quickly” if he can do so using only O(log n…

## 63 Citations

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This work considers a version of the game “Twenty Questions” played on the set {0,…,N-1} where the player giving answers may lie in her answers, and gives precise conditions for tight bounds on r and optimal bounds on Q under which the questioner has a winning strategy in the game.

### The entropy of lies: playing twenty questions with a liar

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Near optimal strategies are designed that only use comparison queries of the form `$x \leq c$?' for $c\in[n]$ where sorting algorithms in the presence of adversarial noise are derived.

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A set of 1.25n+o(n) questions is given such that for every distribution π, Bob can implement an optimal strategy for π using only questions from $$\mathcal{Q}$$ .

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A basic combinatorial interpretation of Shannon’s entropy function is via the “20 questions” game. This cooperative game is played by two players, Alice and Bob: Alice picks a distribution π over the…

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