Ulam's pathological liar game with one half-lie
We introduce a dual game to Ulam's liar game and consider the case of one half-lie. In the original Ulam's game, Paul attempts to isolate a distinguished element by disqualifying all but one of n possibilities with q yes-no questions, while the responder Carole is allowed to lie a fixed nu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204306204 |
| Summary: | We introduce a dual game to Ulam's liar game and consider
the case of one half-lie. In the original Ulam's game, Paul
attempts to isolate a distinguished element by disqualifying
all but one of n possibilities with q yes-no questions, while the responder Carole is allowed to lie a fixed
number k of times. In the dual game, Paul attempts to prevent
disqualification of a distinguished element by pathological liar
Carole for as long as possible, given that a possibility associated
with k+1 lies is disqualified. We consider the half-lie variant
in which Carole may only lie when the true answer is no. We
prove the equivalence of the dual game to the problem of covering
the discrete hypercube with certain asymmetric sets. We define
A1*(q) for the case k=1 to be the minimum number n such that
Paul can prevent Carole from disqualifying all n elements in q
rounds of questions, and prove that A1*(q)~2q+1/q. |
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| ISSN: | 0161-1712 1687-0425 |