Pseudorandom Bits for Oblivious Branching Programs

TL;DR

This paper introduces a new pseudorandom generator that effectively fools read-$k$ and linear length oblivious branching programs with significantly shorter seed lengths, advancing derandomization techniques.

Contribution

It presents the first constructions of pseudorandom generators with sublinear seed lengths for these models, assuming the read sequence is known in advance.

Findings

Seed length $ ilde{O}(n^{1-1/2^{k-1}})$ for read-$k$ models

Seed length $O(n/ \log \log n)$ for linear length models

Improves upon previous seed length $(1- ext{O}(1))n$ constructions

Abstract

We construct a pseudorandom generator which fools read-$k$ oblivious branching programs and, more generally, any linear length oblivious branching program, assuming that the sequence according to which the bits are read is known in advance. For polynomial width branching programs, the seed lengths in our constructions are $\tilde{O}(n^{1-1/2^{k-1}})$ (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 $(1-\Omega(1))n$.