Efficient read-restricted monotone CNF/DNF dualization by learning with membership queries

We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times (`read-k' monotone CNF). Let f: {0,1}ⁿ→{0,1} 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∈{0,1}^N. The algorithm yields an incremental polynomial output time solution to the (read-k) monotone CNF/DNF dualization problem. The unrestricted versions remain open problems of importance.