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Ulam's searching game with lies

Jurek Czyzowicz, Daniele Mundici, Andrzej Pelc
1989 Journal of combinatorial theory. Series A  
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  ...  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".  ... 
doi:10.1016/0097-3165(89)90062-9 fatcat:vdaorbsekvaznpgw6h46oxe6cq

Ulam's searching game with two lies

Wojciech Guzicki
1990 Journal of combinatorial theory. Series A  
This solves completely the problem of Ulam on 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.  ... 
doi:10.1016/0097-3165(90)90002-e fatcat:cp55swe6zrcpzajuyhce2lizka

Ulam's searching game with three lies

Alberto Negro, Matteo Sereno
1992 Advances in Applied Mathematics  
In the present paper we give a solution of 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.  ... 
doi:10.1016/0196-8858(92)90019-s fatcat:frwtnvc6xfdf3huroiurdcxnjq

Ulam's searching game with a fixed number of lies

Joel Spencer
1992 Theoretical Computer Science  
., 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.  ... 
doi:10.1016/0304-3975(92)90270-p fatcat:4dedps3amzdirdnapvyddt6i3u

Solution of Ulam's searching game with three lies or an optimal adaptive strategy for binary three-error-correcting codes

Christian Deppe
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 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] .  ... 
doi:10.1016/s0012-365x(00)00109-6 fatcat:tewxgtrb4ngdrjsxnglgwt4jyi

An algorithm for "Ulam's Game" and its application to error correcting codes

Eugene L. Lawler, Sergei Sarkissian
1995 Information Processing Letters  
A near-optimal algorithm for "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  ... 
doi:10.1016/0020-0190(95)00127-x fatcat:n5hhedlrf5cafgwf45yauys7cu

Detecting errors in searching games

Andrzej Pelc
1989 Journal of combinatorial theory. Series A  
In the second 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  ... 
doi:10.1016/0097-3165(89)90075-7 fatcat:czgeqjzafnhxnjhmymnj7zml24

Searching with lies: the Ulam problem

Ray Hill, Jehangir P. Karim
1992 Discrete Mathematics  
Karim, 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.  ... 
doi:10.1016/0012-365x(92)90554-s fatcat:7kkogy22fnbmfc4kxatzekizwy

Optimal comparison strategies in Ulam's searching game with two errors

Daniele Mundici, Alberto Trombetta
1997 Theoretical Computer Science  
Since no strategy can find the unknown x E (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  ...  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) .  ... 
doi:10.1016/s0304-3975(97)00030-3 fatcat:sne5op44drbdrcoi427srq2tnu

Ulam's pathological liar game with one half-lie

Robert B. Ellis, Catherine H. Yan
2004 International Journal of Mathematics and Mathematical Sciences  
We introduce a dual 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.  ... 
doi:10.1155/s0161171204306204 fatcat:czs42ada5vh7vchpwqdejnpb4e

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.  ... 

Strategy in Ulam's Game and Tree Code Give Error-Resistant Protocols [article]

Marcin Peczarski
2004 arXiv   pre-print
The construction is based on a generalization of the well known 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.  ... 
arXiv:cs/0410043v1 fatcat:dptmsabz5fhzflo7eahmkyur3a

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.  ... 

On error correction with feedback under list decoding

Ofer Shayevitz
2009 2009 IEEE International Symposium on Information Theory  
This version of the "twenty questions 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  ... 
doi:10.1109/isit.2009.5205965 dblp:conf/isit/Shayevitz09 fatcat:gbwbzbdkzrcozcult62pmco72u

Solution of Ulam's problem on binary search with two lies

Jurek Czyzowicz, Andrzej Pelc, Daniele Mundici
1988 Journal of combinatorial theory. Series A  
We prove that 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  ... 
doi:10.1016/0097-3165(88)90065-9 fatcat:w4gnnpwktzf5jh3r5ojwvgvwey
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