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.
- Pub Date:
- April 2002
- Computer Science - Data Structures and Algorithms;
- Computer Science - Computational Complexity;
- Removed some minor errors. A shorter version of this paper appears in: Proceedings of the 34th ACM Symposium on Theory of Computing (STOC-02), May 19-21, 2002, Montreal, Quebec, Canada