Search problems in the decision tree model

The relative power of determinism, randomness, and nondeterminism for search problems in the Boolean decision tree model is studied. It is shown that the CNF search problem is complete for all the variants of decision trees. It is then shown that the gaps between the nondeterministic, the randomized, and the deterministic complexities can be arbitrarily large for search problems. The special case of nondeterministic complexity is discussed.< >