220 search results - page 1 / 44 » New degree bounds for polynomial threshold functions |
STOC
2003
ACM
14 years 9 months ago
2003
ACM
A real multivariate polynomial p(x1, . . . , xn) is said to sign-represent a Boolean function f : {0, 1}n {-1, 1} if the sign of p(x) equals f(x) for all inputs x {0, 1}n. We gi...
COCO
2010
Springer
14 years 16 days ago
2010
Springer
Abstract. We prove asymptotically optimal bounds on the Gaussian noise sensitivity of degree-d polynomial threshold functions. These bounds translate into optimal bounds on the Gau...
COCO
2003
Springer
14 years 2 months ago
2003
Springer
In this paper we give new extremal bounds on polynomial threshold function (PTF) representations of Boolean functions. Our results include the following: • Almost every Boolean ...
COCO
2010
Springer
14 years 1 months ago
2010
Springer
We give a “regularity lemma” for degree-d polynomial threshold functions (PTFs) over the Boolean cube {−1, 1}n . Roughly speaking, this result shows that every degree-d PTF ...
MFCS
2010
Springer
13 years 7 months ago
2010
Springer
We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute va...