See this document in CiteSeerX!

The Correlation Between Parity and Quadratic Polynomials  (Make Corrections)  
Mod 3 Frederic Green Department of Mathematics and Computer Science Clark...



  Home/Search   Context   Related

 
View or download:
clarku.edu/~fgreen/papers/quad.ps
Cached:  PS.gz  PS  PDF   Image  Update  Help

From:  clarku.edu/~fgreen/paper...papers (more)
(Enter author homepages)

Rate this article: (best)
  Comment on this article  
(Enter summary)

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)

Active bibliography (related documents):   More   All
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)

Similar documents based on text:   More   All
0.4:   Complements of Multivalued Functions - Fenner, Green, Homer, Selman.. (1996)   (Correct)
0.4:   Complex Fourier Technique for Lower Bounds on the Mod-m Degree - Green   (Correct)
0.4:   Relativized Separation of EQP from P^NP - Green, Pruim   (Correct)

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)

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC