Instructor : Emanuele Viola Scribe : Eric Miles Parity requires large constant - depth circuits ( II ) Correlation bounds for parity
نویسنده
چکیده
Then, let q(x) = ∑ m∈M (am ·m(x)) be the weighted sum of these monomials, for a set of weights {am}m∈M . We want to choose the weights in order to give q the properties already stated, which is equivalent to finding a non-trivial solution to a certain system of equations. Denote S = {s1, . . . , s|S|} and M = {m1, . . . ,m|M |}. Then, the system of equations we would like to solve is m1(s1) m2(s1) · · · m|M |(s1) m1(s2) m2(s2) · · · m|M |(s2) .. . . . m1(s|S|) m2(s|S|) · · · m|M |(s|S|) a1 a2 .. a|M | = 0 0 .. 0
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