Efficient threshold circuits for power series

We show that functions with convergent real power series can be well approx imated by two classes of polynomial-size small-weight threshold circuits: d epth-three circuits with threshold gates on all levels and depth-four circu its with threshold gates on the first two levels and AND-OR gates on the la st two. This is done without restricting the input to a fixed closed subint erval of the interval of convergence of the series. We also point out that rational functions and the logarithm of x in base b can be well approximate d by the same classes of circuits when both x and b are given as input. (C) 1999 Academic Press.