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Small-Bias Spaces for Group Products

By Raghu Meka and David Zuckerman


Small-bias, or ɛ-biased, spaces have found many applications in complexity theory, coding theory, and derandomization. We generalize the notion of small-bias spaces to the setting of group products. Besides being natural, our extension captures some of the difficulties in constructing pseudorandom generators for constant-width branching programs- a longstanding open problem. We provide an efficient deterministic construction of small-bias spaces for solvable groups. Our construction exploits the fact that solvable groups have nontrivial normal subgroups that are abelian and builds on the construction of Azar et al. [AMN98] for abelian groups. For arbitrary finite groups, we give an efficient deterministic construction achieving constant bias. We also construct pseudorandom generators fooling linear functions mod p for primes p.

Year: 2009
DOI identifier: 10.1007/978-3-642-03685-9_49
OAI identifier: oai:CiteSeerX.psu:
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