Testing Low-Degree Polynomials over

We describe an efficient randomized algorithm to test if a given binary function "!$# % &(') *!$#+% is a low-degree polynomial (that is, a sum of low-degree monomials). For a given integer ,.-/# and a given real 0213 , the algorithm queries at 425 687 ,"9;:=< points. If is a polynomial of degree at most , , the algorithm always accepts, and if the value of has to be modified on at least an 0 fraction of all inputs in order to transform it to such a polynomial, then the algorithm rejects with probability at least >=? @ . Our result is essentially tight: Any algorithm for testing degree, polynomials over ACB25D> < must perform E 5 6 7 >=:F< queries.

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