Pseudorandomness for Regular Branching Programs via Fourier Analysis

We present an explicit pseudorandom generator for oblivious, read-once, permutation branching programs of constant width that can read their input bits in any order. The seed length is O(log2 n), where n is the length of the branching program. The previous best seed length known for this model was n 1/2 + o(1), which follows as a special case of a generator due to Impagliazzo, Meka, and Zuckerman (FOCS 2012) (which gives a seed length of s 1/2 + o(1) for arbitrary branching programs of size s). Our techniques also give seed length n 1/2 + o(1) for general oblivious, read-once branching programs of width \(2^{n^{o(1)}}\), which is incomparable to the results of Impagliazzo et al.