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… 

On playing “Twenty Questions” with a liar

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

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

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

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

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

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

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

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.

Searching in the presence of linearly bounded errors

The problem of determining an unknown quantity x by asking “yes-no” questions, where some of the answers may be erroneous, is considered using the framework of chip games and the upper bound on number of comparison questions needed is improved.

Least adaptive optimal search with unreliable tests

...

References

SHOWING 1-10 OF 11 REFERENCES

Searching in the presence of linearly bounded errors

The problem of determining an unknown quantity x by asking “yes-no” questions, where some of the answers may be erroneous, is considered using the framework of chip games and the upper bound on number of comparison questions needed is improved.

Guess a number - with lying

Someone thinks of a number between one and one million (which is just less than 220). Another person is allowed to ask up to twenty questions, to each of which the first person is supposed to answer

Coping with Errors in Binary Search Procedures

Solution of Ulam's problem on searching with a lie

  • A. Pelc
  • Mathematics
    J. Comb. Theory, Ser. A
  • 1987

On Evaluating Boolean Functions with Unreliable Tests

This work considers the problem of evaluating a boolean function P(x1,…,xn), by asking queries of the form “xi=?”, and receiving answers which may not always be truthful, and presents an algorithm with cost O(n+sPE+tPE), where sP is the maximal size of a minterm of P (x) and tP ‘is the maximalsize of a maxterm.

Searching with Known Error Probability

  • A. Pelc
  • Mathematics
    Theor. Comput. Sci.
  • 1989

Balancing vectors in the max norm

It is proven that there exists a choice of signs for which all partial sums have max norm at mostKn1/2 and it is shown that such a choice must be anticipatory—there is no way to choose thei-th sign without knowledge of vj forj>i.

Computing with unreliable information

This work adopts a new approach to the "reconfiguration" approach, in which faults are identified and isolated in real time, and devised algorithms that work despite unreliable information.

Block coding with noiseless feedback

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering, 1964.

Adventures of a Mathematician Charles Scribner's Sons, 1976. vL82] J.H. van Lint. Introduction to Coding Theory

  • Adventures of a Mathematician Charles Scribner's Sons, 1976. vL82] J.H. van Lint. Introduction to Coding Theory
  • 1982