Property Testing: A Learning Theory Perspective
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A local decision test for sparse polynomials
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Testing by implicit learning: a brief survey
Property testing
Testing by implicit learning: a brief survey
Property testing
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ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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We give the first algorithm that is both query-efficient andtime-efficient for testing whether an unknown function f:{0,1}n →{0,1} is an s-sparseGF(2) polynomial versus ε-far from everysuch polynomial. Our algorithm makespoly(s,1/ε) black-box queries tof and runs in time n·poly(s,1/ε). The only previousalgorithm for this testing problem [DLM + 07] usedpoly(s,1/ε) queries, but had running timeexponential in s and super-polynomial in1/ε.Our approach significantly extends the "testing by implicitlearning" methodology of [DLM + 07]. The learningcomponent of that earlier work was a brute-force exhaustive searchover a concept class to find a hypothesis consistent with a sampleof random examples. In this work, the learning component is asophisticated exact learning algorithm for sparse GF(2)polynomials due to Schapire and Sellie [SS96]. A crucial element ofthis work, which enables us to simulate the membership queriesrequired by [SS96], is an analysis establishing new properties ofhow sparse GF(2) polynomials simplify under certainrestrictions of "low-influence" sets of variables.