2 research outputs found
Tree Tribes and Lower Bounds for Switching Lemmas
We show tight upper and lower bounds for switching lemmas obtained by the
action of random -restrictions on boolean functions that can be expressed as
decision trees in which every vertex is at a distance of at most from some
leaf, also called -clipped decision trees. More specifically, we show the
following:
If a boolean function can be expressed as a -clipped
decision tree, then under the action of a random -restriction , the
probability that the smallest depth decision tree for has depth
greater than is upper bounded by .
For every , there exists a function that can be
expressed as a -clipped decision tree, such that under the action of a
random -restriction , the probability that the smallest depth decision
tree for has depth greater than is lower bounded by
, for and , where are universal
constants