We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogona...
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...
This paper addresses the point-wise estimation of differential properties of a smooth manifold S--a curve in the plane or a surface in 3D--assuming a point cloud sampled over S is...
Impagliazzo and Wigderson IW97] have recently shown that if there exists a decision problem solvable in time 2O(n) and having circuit complexity 2 (n) (for all but nitely many n) ...
Polynomial identity testing (PIT) problem is known to be challenging even for constant depth arithmetic circuits. In this work, we study the complexity of two special but natural ...