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- W2097114401 abstract "Define the $MOD_m $-degree of a boolean function F to be the smallest degree of any polynomial P, over the ring of integers modulo m, such that for all 0-1 assignments $vec x$, $F(vec x) = 0$ iff $P(vec x) = 0$. By exploring the periodic property of the binomial coefficients modulo m, two new lower bounds on the $MOD_m $-degree of the $MOD_l $ and $- MOD_m $ functions are proved, where m is any composite integer and l has a prime factor not dividing m. Both bounds improve from sublinear to $Omega (n)$. With the periodic property, a simple proof of a lower bound on the $MOD_m $-degree with symmetric multilinear polynomial of the OR function is given. It is also proved that the majority function has a lower bound $frac{n}{2}$ and the MidBit function has a lower bound $sqrt n $." @default.
- W2097114401 created "2016-06-24" @default.
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- W2097114401 date "1996-02-01" @default.
- W2097114401 modified "2023-10-16" @default.
- W2097114401 title "Lower Bounds on Representing Boolean Functions as Polynomials in $Z_m $" @default.
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- W2097114401 doi "https://doi.org/10.1137/s0895480193255505" @default.
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