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We consider exact learning monotone CNF formulas in whicheach 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 naturalnumber k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily readrestricted) 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 timesolution to the (read-k) monotone CNF/DNF dualization problem. The unrestricted versions remain open problems of importance.

Efficient Read-Restricted Monotone CNF/DNF Dualization by Learning with Membership Queries