Abstract:The Direct Product encoding of a string a ∈ {0, 1} n on an underlying domain V ⊆ ( [n] k ), is a function DP V (a) which 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, 1} k , and our goal is to test whether F is close to a direct product encoding, i.e., whether there exists some a ∈ {0, 1} n such that on most sets S, we have F(S) = DP V (a)(S). A natural test is as follows: select a pair (S, S ′ ) ∈ V according to some under… Show more
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