Eecient Read-restricted Monotone Cnf/dnf Dualization by Learning with Membership Queries Produced as Part of the Esprit Working Group in Neural and Computational Learning Ii, Neurocolt2 27150

We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times (\read-k" monotone CNF). Let f : f0;1g n ! f0;1g be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily read restricted) DNF descriptions of f. The algorithm's only method of obtaining information about f is through membership queries, i.e., by inquiring about the value f (x) for points x 2 f0;1g n. The algorithm yields an incremental polynomial output time solution to the bounded degree hypergraph transversal problem, and the problem of (read-k) monotone CNF/DNF dualization, which remain open problems of importance in the unrestricted case.