We give new pseudorandom generators for emph{regular} read-once branching programs of small width. A branching program is regular if the in-degree of every vertex in it is (0 or) 2. For every width d and length n, our pseudorandom generator uses a seed of length O((logd+loglogn+log(1))logn) to produce n bits that cannot be distinguished from a uniformly random string by any regular width d length n read-once branching program, except with probability . We also give a result for general read-once branching programs, in the case that there are no vertices that are reached with small probability. We show that if a (possibly non-regular) branching program of length n and width d has the property that every vertex in the program is traversed with probability at least on a uniformly random input, then the error of the generator above is at most 22 .
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