Abstract
Given the prime conjunctive normal form (CNF) representation $\phi$ of a monotone Boolean function $f:\{0,1\}^n\to\{0,1\}$, the dualization problem calls for finding the corresponding prime disjunctive normal form representation $\psi$ of f. A very simple method works by multiplying out the clauses of $\phi$ from left to right in some order, simplifying whenever possible by using the absorption law. We show that for any monotone CNF $\phi$, left-to-right multiplication can be done in subexponential time, and for many interesting subclasses of monotone CNFs such as those with bounded size, bounded degree, bounded intersection, bounded conformality, and read-once formula, it can be done in polynomial or quasi-polynomial time.
Published Version
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