Hardness of learning DNFs using halfspaces

The problem of learning t-term DNF formulas (for t = O(1)) has been studied extensively in the PAC model since its introduction by Valiant (STOC 1984). A t-term DNF can be efficiently learnt using a t-term DNF only if t = 1 i.e., when it is an AND, while even weakly learning a 2-term DNF using a constant term DNF was shown to be NP-hard by Khot and Saket (FOCS 2008). On the other hand, Feldman, Guruswami, Raghavendra and Wu (FOCS 2009) showed the hardness of weakly learning a noisy AND using a halfspace – the latter being a generalization of an AND, while Khot and Saket (STOC 2008) showed that an intersection of two halfspaces is hard to weakly learn using any function of constantly many halfspaces. The question of whether a 2-term DNF is efficiently learnable using 2 or constantly many halfspaces remained open.