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Pseudorandom Generators for Regular Branching Programs

Author(s): Braverman, Mark; Rao, Anup; Raz, Ran; Yehudayoff, Amir

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Abstract: 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, except for the first layer. 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 nonregular) 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 2/γ2. 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.
Publication Date: 2014
Citation: Braverman, Mark, Anup Rao, Ran Raz, and Amir Yehudayoff. "Pseudorandom Generators for Regular Branching Programs." SIAM Journal on Computing 43, no. 3 (2014): 973-986. doi:10.1137/120875673
DOI: 10.1137/120875673
ISSN: 0097-5397
EISSN: 1095-7111
Pages: 973 - 986
Type of Material: Journal Article
Journal/Proceeding Title: SIAM Journal on Computing
Version: Author's manuscript

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