We introduce a top-down compilation algorithm for constructing structured DNNF for any Boolean function. With appropriate restrictions, the algorithm can produce various subsets of DNNF such as deterministic DNNF and OBDD. We derive a size upper bound for structured DNNF based on this algorithm and use the result to generalize similar upper bounds known for several Boolean functions in the case of OBDD. We then discuss two realizations of the algorithm that work on CNF formulas. We show that these algorithms have time and space complexities that are exponential in the treewidth and the dual treewidth of the input.
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