Lower bounds for three algorithms for transversal hypergraph generation
Discrete Applied Mathematics
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Given the prime CNF representation φ of a monotoneBoolean function f:{0,1} n→{0,1}, the dualization problem calls for finding thecorresponding prime DNF representation ψ off. A very simple method (called Bergemultiplication [2] [Page 52---53]) works by multiplying outthe clauses of φ from left to right in some order,simplifying whenever possible using the absorption law. Weshow that for any monotone CNF φ, Berge multiplicationcan be done in subexponential time, and for many interestingsubclasses of monotone CNF's such as CNF's with bounded size,bounded degree, bounded intersection, bounded conformality, andread-once formula, it can be done in polynomial or quasi-polynomialtime.