The Hardness of the Expected Decision Depth Problem
Dana Ron, Amir Rosenfeld, and Salil Vadhan
Given a function f over n binary variables, and an ordering of the n variables, we consider the Expected Decision Depth problem. Namely, what is the expected number of bits that need to be observed until the value of the function is determined, when bits of the input are observed according to the given order. Our main finding is that this problem is (essentially) #P-complete. Moreover, the hardness holds even when the function f is represented as a decision tree.