Advanced Algorithms and Complexity :
Lecture 16
Lower Bounds for Game Tree Evaluation
September 17, 2018
Lower Bound for Game Tree Evaluation
A randomized algorithm for game tree evaluation can in fact be viewed as
a probability distribution over deterministic algorithms, because the length
of the computation as well as the number of choices at each step are both
finite. We may imagine that all of these coins are tossed before the beginning
of the execution. The tree T2,k is equivalent to a balanced binary tree all of
whose leaves are at distance 2kfrom the root, and all of whose internal nodes
compute the NOR function.
(x1∨y1)∧(x2∨y2) = (x1∨y1)∨(x2∨y2)
Consider a tree of NOR’s of depth 2k. Let p= (3 −√5)/2 which is a
solution of (1 −p)2=p. Each leaf of the tree is independently set to 1 with
probability p. If each input to a NOR node is independently set to 1 with
probability p, then the probability that its output is 1 is the probability that
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