Top-down lower bounds for depth 3 circuits

We present a top-down lower bound method for depth 3 AND-OR-NOT circuits which is simpler than the previous methods and in some cases gives better lower bounds. In particular we prove that depth 3 AND-OR-NOT circuits that compute PARITY resp. MAJORITY require size at least 2^0.618...√n resp. 2^0.849...√n. This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits