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

Abstract

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 in {0,1}^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.