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01593 am a22002173u 4500 |
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|a Grigorescu, Elena
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|a Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
|e contributor
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|a rubinfeld, ronitt
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|a Grigorescu, Elena
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|a Rubinfeld, Ronitt
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|a Jung, Kyomin
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|a Rubinfeld, Ronitt
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|a A local decision test for sparse polynomials
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|b Elsevier,
|c 2017-04-26T20:25:21Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/108433
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|a An ℓ-sparse (multivariate) polynomial is a polynomial containing at most ℓ-monomials in its explicit description. We assume that a polynomial is implicitly represented as a black-box: on an input query from the domain, the black-box replies with the evaluation of the polynomial at that input. We provide an efficient, randomized algorithm, that can decide whether a polynomial [MathML] given as a black-box is ℓ-sparse or not, provided that q is large compared to the polynomial's total degree. The algorithm makes only queries, which is independent of the domain size. The running time of our algorithm (in the bit-complexity model) is , where d is an upper bound on the degree of each variable. Existing interpolation algorithms for polynomials in the same model run in time . We provide a similar test for polynomials with integer coefficients.
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|a en_US
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|a Article
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|t Information Processing Letters
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