# 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…

## 64 Citations

### On playing “Twenty Questions” with a liar

- Computer ScienceSODA '92
- 1992

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

- Computer Science, MathematicsITCS
- 2021

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.

### Twenty (Short) Questions

- Mathematics, Computer ScienceComb.
- 2019

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 $$\mathcal{Q}$$ .

### Twenty ( Simple ) estions

- Computer Science
- 2017

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…

### Twenty (simple) questions

- Mathematics, Computer ScienceSTOC
- 2017

The first main result shows that for every distribution Π, Bob has a strategy that uses only questions of the form "x < c?" and "x = c?", and uncovers x using at most H(Π)+1 questions on average, matching the performance of Huffman codes in this sense.

### The Statistical Physics of Learning: Phase Transitions and Dynamical Symmetry Breaking

- Education
- 2003

To improve the quality of his decisions, homo sapiens is confronted with the problem of guessing new, non-casual, connections between events [4]. We are interested in the simplest mathematical…

### Searching with a Constant Rate of Malicious Lies

- Mathematics
- 2007

The problem of searching in the presence of errors is modeled as a game between a questioner and a responder. The responder chooses an integer x 2 f1; : : : ; ng; and the questioner has to determine…

### On optimal strategies for searching in presence of errors

- MathematicsSODA '94
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This work provides a strategy for Paul to determine the unknown element using at most one query more than that necessary against an adversarial Carole to solve the q-way search problem for q = 3.

### Liar Games and Coding Theory

- Mathematics
- 2006

This project discusses strategies for which it is possible to solve the liar game using the minimum number of questions and further shows links between the liargame and coding theory.

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