Small Sample Spaces Cannot Fool Low Degree Polynomials
نویسندگان
چکیده
A distribution D on a set S ⊂ Zp -fools polynomials of degree at most d in N variables over Zp if for any such polynomial P , the distribution of P (x) when x is chosen according to D differs from the distribution when x is chosen uniformly by at most in the `1 norm. Distributions of this type generalize the notion of -biased spaces and have been studied in several recent papers. We establish tight bounds on the minimum possible size of the support S of such a distribution, showing that any such S satisfies |S| ≥ c1 · ( ( 2d ) d · log p 2 log ( 1 ) + p )
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