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• W2119867099 abstract "We prove exponentially small upper bounds on the correlation between parity and quadratic polynomials mod 3. One corollary of this is that in order to compute parity, circuits consisting of a threshold gate at the top, mod 3 gates in the middle, and AND gates of fan-in two at the inputs must be of size 2/sup /spl Omega/(n)/. This is the first result of this type for general mod subcircuits with ANDs of fan-in greater than 1. This yields an exponential improvement over a recent result of Alon and Beigel (2001). The proof uses a novel inductive estimate of the relevant exponential sums introduced by Cai et al. (1996). The exponential sum bounds are tight." @default.
• W2119867099 created "2016-06-24" @default.
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• W2119867099 date "2003-06-25" @default.
• W2119867099 modified "2023-09-25" @default.
• W2119867099 title "The correlation between parity and quadratic polynomials mod 3" @default.
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• W2119867099 doi "https://doi.org/10.1109/ccc.2002.1004341" @default.
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