Efficient Read-Restricted Monotone CNF/DNF Dualization by Learning with Membership Queries - Domingo, Carlos; Mishra, Nina; Pitt, Leonard (Machine learning, 1999)
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}^sup n^ [arrow right] {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}^sup 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.[PUBLICATION ABSTRACT]