Nearly Optimal Pseudorandomness From Hardness

Existing proofs that deduce \text{BPP} =\mathrm{P} from circuit lower bounds convert randomized algorithms into deterministic algorithms with a large polynomial slowdown. We convert randomized algorithms into deterministic ones with little slowdown. Specifically, assuming exponential lower bounds ag...

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Bibliographic Details
Published in:Proceedings / annual Symposium on Foundations of Computer Science pp. 1057 - 1068
Main Authors: Doron, Dean, Moshkovitz, Dana, Oh, Justin, Zuckerman, David
Format: Conference Proceeding
Language:English
Published: IEEE 01.11.2020
Subjects:
Computer science
derandomization
Generators
Hybrid power systems
Integrated circuit modeling
list-recoverable codes
Probabilistic logic
pseudo-entropy
pseudorandom generators
Runtime
Testing
ISSN:2575-8454
Online Access:Get full text
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Summary:Existing proofs that deduce \text{BPP} =\mathrm{P} from circuit lower bounds convert randomized algorithms into deterministic algorithms with a large polynomial slowdown. We convert randomized algorithms into deterministic ones with little slowdown. Specifically, assuming exponential lower bounds against randomized single-valued nondeterministic (SVN) circuits, we convert any randomized algorithm over inputs of length n running in time t\geq n to a deterministic one running in time t^{2+\alpha} for an arbitrarily small constant \alpha > 0 . Such a slowdown is nearly optimal, as, under complexity-theoretic assumptions, there are problems with an inherent quadratic derandomization slowdown. We also convert any randomized algorithm that errs rarely into a deterministic algorithm having a similar running time (with pre-processing). The latter derandomization result holds under weaker assumptions, of exponential lower bounds against deterministic SVN circuits. Our results follow from a new, nearly optimal, explicit pseudorandom generator fooling circuits of size s with seed length (1 + α)log s, under the assumption that there exists a function f ∊ E that requires randomized SVN circuits of size at least 2 (1−α')n , where. α=O(α'). The construction uses, among other ideas, a new connection between pseudoentropy generators and locally list recoverable codes.
ISSN:2575-8454
DOI:10.1109/FOCS46700.2020.00102