  We consider the problem of dualizing a monotone CNF (equivalently, computing
all minimal transversals of a hypergraph), whose associated decision problem is
a prominent open problem in NP-completeness. We present a number of new
polynomial time resp. output-polynomial time results for significant cases,
which largely advance the tractability frontier and improve on previous
results. Furthermore, we show that duality of two monotone CNFs can be
disproved with limited nondeterminism. More precisely, this is feasible in
polynomial time with O(chi(n) * log n) suitably guessed bits, where chi(n) is
given by \chi(n)^chi(n) = n; note that chi(n) = o(log n). This result sheds new
light on the complexity of this important problem.
