Pseudorandomness for Linear Length Branching Programs and Stack Machines

Abstract

We show the existence of an explicit pseudorandom generator G of linear stretch such that for every constant k, the output of G is pseudorandom against: Oblivious branching programs over alphabet {0,1} of length kn and size 2 O(n/logn) on inputs of size n. Non-oblivious branching programs over alphabet Σ of length kn, provided the size of Σ is a power of 2 and sufficiently large in terms of k. The model of logarithmic space randomized Turing Machines (over alphabet {0,1}) extended with an unbounded stack that make k passes over their randomness.