It is known that if a Boolean function f in n variables has a DNF and a CNF of size at most N then f also has a (deterministic) decision tree of size exp(O(lognlog2N). We show that this simulation {em cannot} be made polynomial: we exhibit explicit Boolean functions f that require deterministic trees of size exp((log2N)) where N is the total number of monomials in minimal DNFs for f and eg f. Moreover, we exhibit new examples of explicit Boolean functions that require deterministic read-once branching programs of exponential size whereas both the functions and their negations have small nondeterministic read-once branching programs. One example results from the Bruen-Blokhuis bound on the size of nontrivial blocking sets in projective planes: it is remarkably simple and combinatorially clear. Whereas other examples have the additional property that f is in AC^0.
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