TY - GEN

T1 - Pseudorandom generators for regular branching programs

AU - Braverman, Mark

AU - Rao, Anup

AU - Raz, Ran

AU - Yehudayoff, Amir

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2010

Y1 - 2010

N2 - 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/γ 2.

AB - 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/γ 2.

KW - Branching programs

KW - Explicit constructions

KW - Pseudorandomness

UR - http://www.scopus.com/inward/record.url?scp=78751520954&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78751520954&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2010.11

DO - 10.1109/FOCS.2010.11

M3 - Conference contribution

AN - SCOPUS:78751520954

SN - 9780769542447

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 40

EP - 47

BT - Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010

T2 - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010

Y2 - 23 October 2010 through 26 October 2010

ER -