On learning width two branching programs

Abstract

We prove that strict width two branching programs or SW 2 (which are width two branching programs with exactly two sinks, as defined by Borodin et al. (1986)) are properly PAC learnable under any distribution. We also observe that PAC learning monotone width two branching programs (which are width two branching programs with exactly one rejecting sink) is as hard as learning DNF formulae. This work refines both the positive and negative results of the paper by Ergün et al. (1995) and answers one of the open questions in that paper.