Projective DNF formulae and their revision

Abstract

Combinatorial and learnability results are proven for projective disjunctive normal forms, a class of DNF expressions introduced by Valiant. Dedicated to Prof. Peter Hammer on the occasion of his 70th birthday. 1 Introduction The model of projection learning was introduced by Valiant [17], motivated by constraints imposed on learnability by biology. Projection learning aims to learn a target concept over some large domain, in this paper {0, 1} n , by learning some of its projections (or restrictions) to a class of smaller domains, and combining these projections. Valiant proved a general mistake bound for This paper represents an extended and revised version of the conference paper [16].

On k-Term DNF with the Largest Number of Prime Implicants

“…First we note that if a set is not a cube then this fact can be certified by three points (see, e.g., [9] for a precise definition of a certificate and applications of this notion, and [20] for related results).…”