E cient distribution-free learning of Boolean formulae from positive and negative examples is considered. It is shown that classes of formulae that are e ciently learnable from only positive examples or only negative examples have certain closure properties. A new substitution technique is used to show that in the distribution-free case learning DNF disjunctive normal form formulae is no harder than learning monotone DNF. We prove that monomials cannot be e ciently learned from negative examples alone, even if the negative examples are uniformly distributed. It is also shown that if the examples are drawn from uniform distributions then the class of DNF in which each v ariable occurs at most once is e ciently learnable, while the class of all monotone Boolean functions is e ciently weakly learnable i.e., individual examples are correctly classi ed with a probability larger than 1 2 + 1 p , where p is a polynomial in the relevant parameters of the learning problem. We then show an equivalence between the notion of weak learning and the notion of group learning, where a group of examples of polynomial size, either all positive or all negative, must be correctly classi ed with high probability.

A systematic flow is described for characterizing, modeling, and simulating single event transient-induced soft errors in cell-based designs. Pulse broadening effects are quantified for a 65 nm CMOS process. Index Terms-Single Event Transient (SET), Pulse broadening, Soft Error Rate (SER)