  We investigate the randomized decision tree complexity of a specific class of
read-once threshold functions. A read-once threshold formula can be defined by
a rooted tree, every internal node of which is labeled by a threshold function
$T_k^n$ (with output 1 only when at least $k$ out of $n$ input bits are 1) and
each leaf by a distinct variable. Such a tree defines a Boolean function in a
natural way. We focus on the randomized decision tree complexity of such
functions, when the underlying tree is a uniform tree with all its internal
nodes labeled by the same threshold function. We prove lower bounds of the form
$c(k,n)^d$, where $d$ is the depth of the tree. We also treat trees with
alternating levels of AND and OR gates separately and show asymptotically
optimal bounds, extending the known bounds for the binary case.
