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Pseudorandom Generators for Regular Branching Programs

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4 Author(s)
Braverman, M. ; Univ. of Toronto, Toronto, ON, Canada ; Rao, A. ; Raz, R. ; Yehudayoff, A.

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/ϵ)) 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 ϵ. 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 γ on a uniformly random input, then the error of the generator above is at most 2ϵ/γ2.

Published in:

Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on

Date of Conference:

23-26 Oct. 2010

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