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ECCC
2010

Pseudorandom Generators for Regular Branching Programs

13 years 11 months ago
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...
Mark Braverman, Anup Rao, Ran Raz, Amir Yehudayoff
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2010
Where ECCC
Authors Mark Braverman, Anup Rao, Ran Raz, Amir Yehudayoff
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