[PDF][PDF] Hitting sets give two-sided derandomization of small space
A hitting set is a" one-sided" variant of a pseudorandom generator (PRG), naturally suited to
derandomizing algorithms that have one-sided error. We study the problem of using a given
hitting set to derandomize algorithms that have two-sided error, focusing on space-bounded
algorithms. For our first result, we show that if there is a log-space hitting set for polynomial-
width read-once branching programs (ROBPs), then not only does π= ππ, but π= πππ as
well. This answers a question raised by Hoza and Zuckerman [William M. Hoza and DavidοΏ½β¦
derandomizing algorithms that have one-sided error. We study the problem of using a given
hitting set to derandomize algorithms that have two-sided error, focusing on space-bounded
algorithms. For our first result, we show that if there is a log-space hitting set for polynomial-
width read-once branching programs (ROBPs), then not only does π= ππ, but π= πππ as
well. This answers a question raised by Hoza and Zuckerman [William M. Hoza and DavidοΏ½β¦
Abstract
A hitting set is a" one-sided" variant of a pseudorandom generator (PRG), naturally suited to derandomizing algorithms that have one-sided error. We study the problem of using a given hitting set to derandomize algorithms that have two-sided error, focusing on space-bounded algorithms. For our first result, we show that if there is a log-space hitting set for polynomial-width read-once branching programs (ROBPs), then not only does π= ππ, but π= πππ as well. This answers a question raised by Hoza and Zuckerman [William M. Hoza and David Zuckerman, 2018].
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