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1999
IEEE

Near-Optimal Conversion of Hardness into Pseudo-Randomness

8 years 7 months ago
Near-Optimal Conversion of Hardness into Pseudo-Randomness
Various efforts ([?, ?, ?]) have been made in recent years to derandomize probabilistic algorithms using the complexity theoretic assumption that there exists a problem in E = dtime(2O(n) ), that requires circuits of size s(n), (for some function s). These results are based on the NW-generator [?]. For the strong lower bound s(n) = 2 n , [?], and later [?] get the optimal derandomization, P = BPP. However, for weaker lower bound functions s(n), these constructions fall far short of the natural conjecture for optimal derandomization, namely that bptime(t) dtime(2O(s-1 (t)) ). The gap in these constructions is due to an inherent limitation on efficiency in NW-style pseudo-random generators. In this paper we are able to get derandomization in almost optimal time using any lower bound s(n). We do this by using the NW-generator in a new, more sophisticated way. We view any failure of the generator as a reduction from the given "hard" function to its restrictions on smaller input...
Russell Impagliazzo, Ronen Shaltiel, Avi Wigderson
Added 03 Aug 2010
Updated 03 Aug 2010
Type Conference
Year 1999
Where FOCS
Authors Russell Impagliazzo, Ronen Shaltiel, Avi Wigderson
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