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/log n) on inputs of size n. - Non-oblivious branching programs over alphabet ∑ of length kn, provided the size of ∑ 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. The construction of the pseudorandom generator G is the same as in our previous work (FOCS 2011). The results here rely on a stronger analysis of the construction. For the last result we give a length-efficient simulation of stack machines by non-deterministic branching programs. (over a large alphabet) whose accepting computations have a unique witness. © 2012 Springer-Verlag.