On learning Boolean functions

This paper deals with the learnability of Boolean functions. An intuitively appealing notion of dimensionality is developed and used to identify the most general class of Boolean function families that are learnable from polynomially many positive examples with one-sided error. It is then argued that although bounded DNF expressions lie outside this class, they must have efficient learning algorithms as they are well suited for expressing many human concepts. A framework that permits efficient learning of bounded DNF functions is identified.