Amplification and percolation (probabilistic Boolean functions)

The authors extend R.B. Boppana's results (1989) in two ways. They first show that his two lower bounds hold for general read-once formulae, not necessarily monotone, that may even include exclusive-or gates. They are then able to join his two lower bounds together and show that any read-once, not necessarily monotone, formula that amplifies (p-/sup 1///sub n/,p+/sup 1///sub n/) to (2/sup -n/,1-2/sup -n/) has size of at least Omega (n/sup alpha +2/). This result does not follow from Boppana's arguments and it shows that the amount of amplification achieved by L.G. Valiant (1984) is the maximal achievable using read-once formulae.<
>