Exact learning of DNF formulas using DNF hypotheses

Abstract

(MATH) We show the following: For any e (3 + e)-term DNF cannot be polynomial-query learned with membership and strongly proper equivalence queries. For any function f(n) e o [box] (/frac√n \over log n) [end-box] , m-term DNF formulas cannot be polynomial-query learned by a membership and equivalence query algorithm that uses m … f(n)-term DNF formulas as hypotheses. Read-thrice DNF formulas are not learnable with membership and proper equivalence queries. log n-term DNF formulas can be polynomial-query learned with membership and proper equivalence queries. (This complements a result of Bshouty, Goldman, Hancock, and Matar stating that [box] √log n [end-box] -term DNF can be so learned in polynomial time. Using purely information theoretic techniques, these results extend and improve what is currently known. (For example, a weaker version of (a) was known only under a barely plausible complexity theoretic assumption, (b) was previously unknown, and (c) was known under the assumption P † NP.)