220 search results - page 1 / 44 » New degree bounds for polynomial threshold functions |
STOC
2003
ACM
14 years 7 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
13 years 10 months 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 20 days 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
13 years 11 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 5 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...