Deterministic approximate counting of depth-2 circuits

Abstract

The authors describe deterministic algorithms which for a given depth-2 circuit F approximate the probability that on a random input F outputs a specific value alpha . The approach gives an algorithm which for a given GF(2) multivariate polynomial p and given in >0 approximates the number of zeros (or ones) of p within a multiplicative factor 1+ in . The algorithm runs in time exp(exp(O( square root log(n/ in )))), where n is the size of the circuit. They also obtain an algorithm which given a DNF formula F and in >0 approximates the number of satisfying assignments of F within a factor of 1+ in and runs in time exp(O((log(n/ in ))/sup 4/)).<>