Ulam's searching game with three lies

Negro, Alberto; Sereno, Matteo

doi:10.1016/0196-8858(92)90019-s

Cited by 25 publications

(8 citation statements)

References 6 publications

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“…If ch(0, t 1 , t 2 , t 3 ) ≤ 12 then σ is 4-intervals nice unless it is one of the states in Table 1. [18]. This set coincides with the set of types of well shaped states that are 0-typical but non 4-interval nice.…”

mentioning

confidence: 72%

“…Definition 8 (0-typical state [13] [18]) Let σ be a state of type (t 0 , t 1 , t 2 , t 3 ) with ch(t 0 , t 1 , t 2 , t 3 ) = q. We say that σ is 0-typical if the following hold…”

Section: The Proof Of the Main Theoremmentioning

confidence: 99%

“…We then show how to refine our main tool to turn the above asymptotic result into a complete characterization of the instances of the Ulam-Rényi game with 4-interval question and 3 lies that admit strategies using the theoretical minimum number of questions. For this, we build upon the result of [18] and show that if there exists a strategy for the classical Ulam-Rényi game with 3 lies over a serach space that uses the information theoretic minimum number of questions, then the same strategy can be implemented using only 4-interval questions.…”

Section: Introductionmentioning

confidence: 99%

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On the multi-interval Ulam-Rényi game: For 3 lies 4 intervals suffice

Cicalese

Rossi

2020

Theoretical Computer Science

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We study the problem of identifying an initially unknown m-bit number by using yes-no questions when up to a fixed number e of the answers can be erroneous. In the variant we consider here questions are restricted to be the union of up to a fixed number of intervals.For any e ≥ 1 let ke be the minimum k such that for all sufficiently large m, there exists a strategy matching the information theoretic lower bound and only using k-interval questions. It is known that ke = O(e 2 ) and it has been conjectured that the ke = Θ(e). This linearity conjecture is supported by the known results for small values of e as for e ≤ 2 we have ke = e. We focus on the case e = 3 and show k3 ≤ 4 improving upon the previously known bound k3 ≤ 10.

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mentioning

confidence: 72%

“…Definition 8 (0-typical state [13] [18]) Let σ be a state of type (t 0 , t 1 , t 2 , t 3 ) with ch(t 0 , t 1 , t 2 , t 3 ) = q. We say that σ is 0-typical if the following hold…”

Section: The Proof Of the Main Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the multi-interval Ulam-Rényi game: For 3 lies 4 intervals suffice

Cicalese

Rossi

2020

Theoretical Computer Science

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“…There are many papers dealing with the Rényi-Ulam's game. The exact values of L(n, 2, 1), L(n, 2, 2) and L(n, 2, 3) have been determined by Pelc [15], Guzicki [8] and Deppe [7], respectively, building on previous work by Czyzowicz et al [5,6], Negro and Sereno [13,14] and others (see Pelc's survey [17], Hill [9], Cicalese et al [4]). For arbitrary fixed number of lies, Spencer [18] determined the value of L(n, q, e) for sufficiently large integer n. For q = 3, the exact values of L(n, 3, 1) and L(n, 3, 2) have been determined by Pelc [16] and Liu et al [10], respectively, in terms of coin-weighing problem.…”

Section: Introductionmentioning

confidence: 99%

Q-ary search with one lie and bi-interval queries

Liu

Meng

Xing

2007

Information Processing Letters

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“…Optimal solutions (for each m) are given in [9,15,16,21], respectively, for the cases = 1, = 2, = 3, and (for all sufficiently large m) for the general case. See [10] for a survey.…”

Section: Introductionmentioning

confidence: 99%

Perfect Two-Fault Tolerant Search with Minimum Adaptiveness

Cicalese¹,

Mundici²

2000

Advances in Applied Mathematics

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Our aim is to minimize the number of answer/question alternations in a perfect two-fault-tolerant search. Ulam and Rényi posed the problem of searching for an unknown m-bit number by asking the minimum number of yes-no questions, when up to of the answers may be erroneous/mendacious. Berlekamp considered the same problem in the context of error-correcting communication with feedback. Among others, he proved that at least q m questions are necessary, where q m is the smallest integer q satisfying 2 q−m ≥ j=0 q j. When all questions are asked in advance, and adaptiveness has no role, finding a perfect strategy (i.e., a strategy with q m questions) amounts to finding an -error-correcting code with 2 m codewords of length q m . From coding theory it is known that such perfect non-adaptive searching strategies are rather the exception, for ≥ 2. At the other extreme, in a fully adaptive search, where the t + 1 th question is asked knowing the answer to the tth question, perfect strategies are known to exist for all sufficiently large m.1 A preliminary draft of the first part of this paper, only dealing with binary search, appears in [7].2 Partially supported by an ENEA grant. 3 Partially supported by COST ACTION 15 on many-valued logics for computer science applications, and by the Italian MURST Project on Logic. cicalese and mundiciWhat happens if we impose restrictions on the amount of adaptiveness avaliable to the questioner? Focusing attention on the case = 2, we shall prove that, for each m = 2, perfect searching strategies still exist even if the questioner is allowed to adapt his strategy only once. All our results are constructive and explicitly yield perfect two-error-correcting codes with the least possible feedback. We finally generalize our results to k-ary search.

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Ulam's searching game with three lies

Cited by 25 publications

References 6 publications

On the multi-interval Ulam-Rényi game: For 3 lies 4 intervals suffice

On the multi-interval Ulam-Rényi game: For 3 lies 4 intervals suffice

Q-ary search with one lie and bi-interval queries

Perfect Two-Fault Tolerant Search with Minimum Adaptiveness

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