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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 . This is the first result of this type for general mod 3 subcircuits with ANDs of fan-in greater than 1. This yields an exponential improvement over a long-standing result of Smolensky,... (Update)
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1.3: Lower Bounds for Approximations by Low Degree Polynomials over.. - Alon, Beigel (2001) (Correct)
1.0: Exponential Sums and Circuits with a Single Threshold Gate and.. - Green (1999) (Correct)
0.4: On the Correlation of Symmetric Functions - Cai, Green, Thierauf (1996) (Correct)
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BibTeX entry: (Update)
@misc{ green-correlation,
author = "Mod Frederic Green",
title = "The Correlation Between Parity and Quadratic Polynomials",
url = "citeseer.ist.psu.edu/602654.html" }
Citations (may not include all citations):189 Algebraic methods in the theory of lower bounds for Boolean .. (context) - Smolensky - 1987
126 PP is as hard as the polynomial-time hierarchy (context) - Toda - 1991
115 Separating the polynomial-time hierarchy by oracles (context) - Yao - 1985
114 Bounded-width polynomial-size branching programs recognize e.. (context) - Barrington - 1989
97 Encyclopedia of Mathematics and its Applications (context) - Lidl, Niederreiter et al. - 1983
77 Threshold circuits of bounded depth (context) - Hajnal, Maass et al. - 1987
75 and the polynomial-time hierarchy (context) - Furst, Saxe et al. - 1984
68 On ACC and threshold circuits (context) - Yao - 1990
65 A note on the power of threshold circuits (context) - Allender - 1989
61 Natural proofs - Razborov, Rudich - 1994
54 Lower bounds on the size of bounded depth networks over a co.. (context) - Razborov - 1987
39 pseudorandom generators for logspace (context) - Babai, Nisan et al. - 1992
19 Computational limitations of small-depth circuits (context) - astad - 1987
18 the computational power of depth 2 circuits with threshold a.. - Krause, Pudl et al. - 1994
15 the power of small-depth threshold circuits - astad, Goldmann - 1991
10 Complex polynomials and circuit lower bounds for modular cou.. (context) - Barrington, Straubing - 1994
8 A note on the power of majority gates and modular gates (context) - Goldmann - 1995
3 Upper and lower bounds for some depth-3 circuit classes - Beigel, Maciel - 1997
3 With probability one (context) - Cai - 1989
3 the correlation of symmetric functions - Cai, Green et al. - 1996
2 Exponential sums and circuits with a single threshold gate a.. - Green - 1999
1 The power of the middle bit of a #P function - Green, obler et al. - 1995
1 A complex-number fourier method for lower bounds on the Mod-.. (context) - Green - 2000
1 Equations over nite elds: An elementary approach (context) - Schmidt - 1976
1 Lower bounds for approximations by low degree polynomials ov.. - Alon, Beigel - 2001
1 A weight-size trade-o for circuits with mod m gates (context) - Grolmusz - 1994
Documents on the same site (http://math.clarku.edu/~fgreen/papers/papers.html):
Relativized Separation of EQP from P^NP - Green, Pruim (Correct)
The Power of the Middle Bit of a #P Function - Green, Köbler, Regan.. (1997) (Correct)
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