We study the link between the complexity of a polynomial and that of its coefficient functions. Valiant’s theory is a good setting for this, and we start by generalizing one of V...
Abstract. It is shown that high-order feedforward neural nets of constant depth with piecewisepolynomial activation functions and arbitrary real weights can be simulated for Boolea...
: The Game of Life cellular automaton is a classical example of a massively parallel collision-based computing device. The automaton exhibits mobile patterns, gliders, and generato...
We show that any k-wise independent probability distribution on {0, 1}n O(m2.22− √ k/10)fools any boolean function computable by an m-clause DNF (or CNF) formula on n variable...
We prove two main results on how arbitrary linear threshold functions f(x) = sign(w · x − θ) over the n-dimensional Boolean hypercube can be approximated by simple threshold f...