Tight Bounds on Proper Equivalence Query Learning of DNF

We prove a new structural lemma for partial Boolean functions \emphf, which we call the \emphseed lemma for \emphDNF. Using the lemma, we give the first subexponential algorithm for proper learning of poly(\emphn)-term DNF in Angluin’s Equivalence Query (EQ) model. The algorithm has time and query complexity 2^(Õ√\emphn), which is optimal. We also give a new result on certificates for DNF-size, a simple algorithm for properly PAC-learning DNF, and new results on EQ-learning log \emphn-term DNF and decision trees.