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2013 | OriginalPaper | Chapter

Search When the Lie Depends on the Target

Authors : Gyula O. H. Katona, Krisztián Tichler

Published in: Information Theory, Combinatorics, and Search Theory

Publisher: Springer Berlin Heidelberg

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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.

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Metadata
Title
Search When the Lie Depends on the Target
Authors
Gyula O. H. Katona
Krisztián Tichler
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-36899-8_32

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