Exact Learning from Membership Queries: Some Techniques, Results and New Directions

Bshouty, Nader H.

doi:10.1007/978-3-642-40935-6_4

Cited by 7 publications

(3 citation statements)

References 74 publications

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“…Assuming a set of (n, (s, r))-CFF of size N can be constructed in time T , this algorithm learns s-term r-MDNF with N queries in time O( n r + T ). In [20,9], it is shown that any set A ⊂ {0, 1} n that non-adaptively learns s-term r-MDNF is an (n, (s − 1, r))-CFF. Therefore, the minimum size of an (n, (s − 1, r))-CFF is also a lower bound for the number of queries (and therefore also for the time) for non-adaptively learning s-term r-MDNF.…”

Section: Introductionmentioning

confidence: 99%

Non-adaptive learning of a hidden hypergraph

Abasi

Bshouty

Mazzawi

2018

Theoretical Computer Science

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Section: Introductionmentioning

confidence: 99%

Non-adaptive learning of a hidden hypergraph

Abasi

Bshouty

Mazzawi

2018

Theoretical Computer Science

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“…The above problem is also equivalent to the problem of non-adaptive deterministic (resp. randomized) learning the class of boolean disjunction of up to d variables from membership queries [2].…”

Section: Introductionmentioning

confidence: 99%

“…where m RID is the minimum number of tests in the RID algorithms, e = 2.71828 • • • is the Euler's number and γ d is defined in (2). But again, no polynomial time algorithm is known for such matrix even for the special case when the number of the defective items is exactly d.…”

Section: Introductionmentioning

confidence: 99%

Non-Adaptive Randomized Algorithm for Group Testing

Bshouty¹,

Diab²,

Kawar³

et al. 2017

Preprint

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We study the problem of group testing with a non-adaptive randomized algorithm in the random incidence design (RID) model where each entry in the test is chosen randomly independently from {0, 1} with a fixed probability p. The property that is sufficient and necessary for a unique decoding is the separability of the tests, but unfortunately no linear time algorithm is known for such tests. In order to achieve linear-time decodable tests, the algorithms in the literature use the disjunction property that gives almost optimal number of tests. We define a new property for the tests which we call semi-disjunction property. We show that there is a linear time decoding for such test and for d → ∞ the number of tests converges to the number of tests with the separability property and is therefore optimal (in the RID model). Our analysis shows that, in the RID model, the number of tests in our algorithm is better than the one with the disjunction property even for small d.

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