Complexity Theoretic Limitations on Learning DNF’s

Using the recently developed framework of Daniely, Linial and Shalev-Shwartz, we show that under a natural assumption on the complexity of random K-SAT, learning DNF formulas is hard. Furthermore, the same assumption implies the hardness of various learning problems, including intersections of logarithmically many halfspaces, agnostically learning conjunctions, as well as virtually all (distribution free) learning problems that were previously shown hard (under various complexity assumptions).