Pseudorandom Generators for Regular Branching Programs

We give new pseudorandom generators for regular read-once branching programs of small width. A branching program is regular if the in-degree 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 read-once branching program, except with probability . We also give a result for general read-once branching programs, in the case that there are no vertices that are reached with small probability. We show that if a (possibly non-regular) 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 non-zero entries forms a hitting set for regular width d bran...

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Mark Braverman, Anup Rao, Ran Raz, Amir Yehudayoff
• Keywords: Branching Programs, ECCC 2010, Pseudorandom Generator, Read-once Branching