Pseudorandom Bits for Oblivious Branching Programs

Abstract

We construct a pseudorandom generator that fools known-order read- k oblivious branching programs and, more generally, any linear length oblivious branching program. For polynomial width branching programs, the seed lengths in our constructions are Õ ( n 1−1/2 k−1 ) (for the read- k case) and O ( n / log log n ) (for the linear length case). Previously, the best construction for these models required seed length (1 − Ω(1)) n .