Computing Downwards Accumulations on Trees Quickly

Downwards accumulations on binary trees are essentially functions which pass information down a tree. Under certain conditions, these accumulations are both `efficient' (computable in a functional style in parallel time proportional to the depth of the tree) and `manipulable'. In this paper, we show that these conditions do in fact yield a stronger conclusion: the accumulation can be computed in parallel time proportional to the logarithm of the depth of the tree, on a CREW PRAM machine