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The direct product encoding of a string a 0,1n on an underlying domain V (k[n]) is a function DPV(a) that gets as input a set S V and outputs a restricted to S. In the direct product testing problem, we are given a function F:V 0,1k, and our goal is to test whether F is close to a direct...
Given metric spaces (X, DX) and (Y, DY), an embedding F: X Y is an injective mapping from X to Y. Expansion eF and contraction cF of an embedding F: X Y are defined as eF = maxx;1, x2 ( x1) X DY(F(x1), F(x2))/ DX(x1, x2) and cF = maxx1, x2 ( x1) X DX(x1, x2)/DY(F(x1), F(x2)), respectively,...
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