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Ulam's searching game with lies

1989
*
Journal of combinatorial theory. Series A
*

Hence, looking from the more general point of view of

doi:10.1016/0097-3165(89)90062-9
fatcat:vdaorbsekvaznpgw6h46oxe6cq
*searching**games*admitting*lies*, the above problem of coding theory is that of finding an optimal strategy in a non-interactive*game*, while*Ulam's*problem ... The main objective of the present paper is to give a solution of*Ulam's*problem for two*lies*, in the case when the*search*space has size 2". ...##
###
Ulam's searching game with two lies

1990
*
Journal of combinatorial theory. Series A
*

This solves completely the problem of Ulam on

doi:10.1016/0097-3165(90)90002-e
fatcat:cp55swe6zrcpzajuyhce2lizka
*searching**with*two*lies*, partially solved by Czyzowicz, Mundici, and Pelt. Their solution applied only to the case when n is a power of 2. ... Some asymptotic estimates in the case of more*lies*were, however, obtained by Rivest et al. in [R et al.] , cf. also A. Pelt in [P2].*Ulam's**game*is closely connected*with*coding theory. ... A winning strategy in*Ulam's**game*which allows k*lies*can be considered as an "interactive" counterpart of a k-error-correcting code. ...##
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Ulam's searching game with three lies

1992
*
Advances in Applied Mathematics
*

In the present paper we give a solution of

doi:10.1016/0196-8858(92)90019-s
fatcat:frwtnvc6xfdf3huroiurdcxnjq
*Ulam's*problem for three*lies*, when the*search*space has size 2"'. ... 'This ULAM' S*SEARCHING**GAME**WITH*3*LIES*411 n+3q- 9 i 1 3 2 0; Table IV , IV analysis of the first three levels of the*search*tree is sufficient to prove the lemma. q LEMMA 7. ...##
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Ulam's searching game with a fixed number of lies

1992
*
Theoretical Computer Science
*

.,

doi:10.1016/0304-3975(92)90270-p
fatcat:4dedps3amzdirdnapvyddt6i3u
*Ulam's**searching**game**with*a fixed number of*lies*, Theoretical Computer Science 95 (1992) 3077321. Paul tries to find an unknown x from 1 to n by asking 4 Yes-No questions. ... The original*game*We return to the original*game**with*k*lies*and q moves. In our formulation the original position is P = (n, 0, . . . , 0) . ... In this sense Xi gives a count on those x for which if x is the answer then Carole has already*lied*i times. We like to think of this*game*in terms of chips. ...##
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Solution of Ulam's searching game with three lies or an optimal adaptive strategy for binary three-error-correcting codes

2000
*
Discrete Mathematics
*

In this paper we determine the minimal number of yes-no queries that are needed to ÿnd an unknown integer between 1 and N , if at most three of the answers are

doi:10.1016/s0012-365x(00)00109-6
fatcat:tewxgtrb4ngdrjsxnglgwt4jyi
*lies*. ... The case of three*lies*if N = 1 000 000 is solved in [20] . The case of three*lies*if N = 2 k is solved in [21] . In [15] it is shown how to solve*Ulam's**game*for l = 1; 2; 3; 4 and N = 2 20 . ... Obviously, Berlekamp's quiet-questionnoisy-answer-*game*is equivalent to*Ulam's**game*. Many*search*problems, which are equivalent to a coding problem, can be found in [1, 2] . ...##
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An algorithm for "Ulam's Game" and its application to error correcting codes

1995
*
Information Processing Letters
*

A near-optimal algorithm for "

doi:10.1016/0020-0190(95)00127-x
fatcat:n5hhedlrf5cafgwf45yauys7cu
*Ulam's**Game*" is presented. The relationship between the*game*and multiple error correcting codes is discussed. ... For many cases, codes derived from winning strategies of the*game*are optimal for the communication scheme*with*noisy forward and noiseless feedback channels. ... Introduction The existence of an optimal or near-optimal strategy for playing a cooperative*game*known to us as "*Ulam's**Game*", or the*game*of "Twenty Questions*with*a Liar", has occupied researchers in ...##
###
Detecting errors in searching games

1989
*
Journal of combinatorial theory. Series A
*

In the second

doi:10.1016/0097-3165(89)90075-7
fatcat:czgeqjzafnhxnjhmymnj7zml24
*game*he also needs to determine the number of*lies*if they occurred. We study optimal winning strategies of the Questioner and determine their lengths. ... The Responder may lie up to k times during the entire*search*. In the first*game*the Questioner wins if he finds the unknown number or if he can prove that some answers were false. ... Hence, looking from the more general point of view of*searching**games*admitting*lies*, the above problem of coding theory is that of finding an optimal strategy in a non-interactive*game*, while*Ulam's*problem ...##
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Searching with lies: the Ulam problem

1992
*
Discrete Mathematics
*

Karim,

doi:10.1016/0012-365x(92)90554-s
fatcat:7kkogy22fnbmfc4kxatzekizwy
*Searching**with**lies*: the Ulam problem, Discrete Mathematics 106/107 (1992) 273-283. ...*Ulam's*problem is to determine the minimal number of yes-no queries sufficient to find an unknown integer between 1 and 220 if at most some given number e of the answers may be*lies*. ... We define an e-lie*game*to be one in which up to e*lies*can be told. ...##
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Optimal comparison strategies in Ulam's searching game with two errors

1997
*
Theoretical Computer Science
*

Since no strategy can find the unknown x E (0, 1, . . ,2" -1)

doi:10.1016/s0304-3975(97)00030-3
fatcat:sne5op44drbdrcoi427srq2tnu
*with*less than q(n) questions, our result provides extremely simple optimal*searching*strategies for*Ulam's**game**with*two*lies*-the*game*of ... As proved in this self-contained paper,*with*the exception of n = 2, q(n) is the smallest number q satisfying Berlekamp's inequality This result would disappear if we only allowed questions of the form ... Introduction*Ulam's**game*[7, p. 2811*with*I*lies*has two players, called Questioner and Responder. The players first fix a*search*space S, = { 0, 1, . . . ,2" -1) . ...##
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Ulam's pathological liar game with one half-lie

2004
*
International Journal of Mathematics and Mathematical Sciences
*

We introduce a dual

doi:10.1155/s0161171204306204
fatcat:czs42ada5vh7vchpwqdejnpb4e
*game*to*Ulam's*liar*game*and consider the case of one half-lie. ... We prove the equivalence of the dual*game*to the problem of covering the discrete hypercube*with*certain asymmetric sets. ... This author is also affiliated*with*the Dalian University of Technology. ...##
###
Page 1784 of Mathematical Reviews Vol. , Issue 94c
[page]

1994
*
Mathematical Reviews
*

In

*Ulam’s**game**with**lies*, a number in S = {0,1,---,2” —1} is to be guessed by asking questions that are answered yes or no,*with*up to k*lies*permitted. ... Daniel Elliott Loeb (Talence) 94c:90133 90D40 03B50 68P10 Mundici, Daniele (I-MILAN-I; Milan) The logic of*Ulam’s**game**with**lies*. ...##
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Strategy in Ulam's Game and Tree Code Give Error-Resistant Protocols
[article]

2004
*
arXiv
*
pre-print

The construction is based on a generalization of the well known

arXiv:cs/0410043v1
fatcat:dptmsabz5fhzflo7eahmkyur3a
*Ulam's**game*. We show equivalence between winning strategies in this*game*and robust protocols for multi-party computation. ... For standard*Ulam's**game*, if Carole is required to make sure that the fraction of*lies*is less than 1/3 of her answers then Paul has a winning strategy*with*Θ(q) questions, where q = ⌈log 2 n⌉ is the number ...*Ulam's**game*is widely considered in connection*with*one-direction data transmission over noisy channel and error correcting codes. ...##
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Page 3382 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

Since no strat- egy can find the unknown x € {0,1,---,2” — 1}

*with*less than q(n) questions, our result provides extremely simple optimal*searching*strategies for*Ulam’s**game**with*two*lies*—the*game*of ... ’s*searching**game**with*two errors. ...##
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On error correction with feedback under list decoding

2009
*
2009 IEEE International Symposium on Information Theory
*

This version of the "twenty questions

doi:10.1109/isit.2009.5205965
dblp:conf/isit/Shayevitz09
fatcat:gbwbzbdkzrcozcult62pmco72u
*game*"*with**lies*is known as*Ulam's**game*[14] . ... This result can be interpreted as follows: If*Ulam's**game**with*t*lies*can be won*with*n questions under a list-of-L and using only Λ L strategies, then the*game**with*t − π L*lies*can be won using only ...##
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Solution of Ulam's problem on binary search with two lies

1988
*
Journal of combinatorial theory. Series A
*

We prove that

doi:10.1016/0097-3165(88)90065-9
fatcat:w4gnnpwktzf5jh3r5ojwvgvwey
*Ulam's*problem has the following solution: THEOREM. ... A Ulam set (*with*at most two*lies*) is a triplet U = (X, Y, Z) of pairwise disjoint finite subsets of KJ. A yes-no question is a subset Q of N. ...*searching**game**with**lies*" (first submitted in March 1986), where the authors solve the general Ulam problem on the least number of yes-no questions sufficient to find a number between I and 2", if up ...
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