Search When the Lie Depends on the Target

  • Gyula O. H. Katona
  • Krisztián Tichler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7777)


The following model is considered. There is exactly one unknown element in the n-element set. A question is a partition of S into three classes: (A,L,B). If x ∈ A then the answer is “yes” (or 1), if x ∈ B then the answer is “no” (or 0), finally if x ∈ L then the answer can be either “yes” or “no”. In other words, if the answer “yes” is obtained then we know that x ∈ A ∪ L while in the case of “no” answer the conclusion is x ∈ B ∪ L. The mathematical problem is to minimize the minimum number of questions under certain assumptions on the sizes of A,B and L. This problem has been solved under the condition |L| ≥ k by the author and Krisztián Tichler in previous papers for both the adaptive and non-adaptive cases. In this paper we suggest to solve the problem under the conditions |A| ≤ a, |B| ≤ b. We exhibit some partial results for both the adaptive and non-adaptive cases. We also show that the problem is closely related to some known combinatorial problems. Let us mention that the case b = n − a has been more or less solved in earlier papers.


combinatorial search search with lies 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Gyula O. H. Katona
    • 1
  • Krisztián Tichler
    • 2
  1. 1.Rényi InstituteBudapestHungary
  2. 2.Eötvös UniversityBudapestHungary

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