 
Summary: Pseudorandom Generators for Regular Branching Programs
Mark Braverman
Anup Rao
Ran Raz
Amir Yehudayoff§
Abstract
We give new pseudorandom generators for regular readonce branching programs of small
width. A branching program is regular if the indegree of every vertex in it is either 0 or 2.
For every width d and length n, our pseudorandom generator uses a seed of length O((log d +
log log n + log(1/ )) log n) to produce n bits that cannot be distinguished from a uniformly
random string by any regular width d length n readonce branching program, except with
probability .
We also give a result for general readonce branching programs, in the case that there are
no vertices that are reached with small probability. We show that if a (possibly nonregular)
branching program of length n and width d has the property that every vertex in the program
is traversed with probability at least on a uniformly random input, then the error of the
generator above is at most 2 /2
.
Finally, we show that the set of all binary strings with less than d nonzero entries forms a
hitting set for regular width d branching programs.
