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- W2397366471 abstract "A recurring theme in the literature on derandomization is that probabilistic algorithms can be simulated quickly by deterministic algorithms, if one can obtain impressive (i.e., superpolynomial, or even nearly-exponential) circuit size lower bounds for certain problems. In contrast to what is needed for derandomization, existing lower bounds seem rather (linear-size lower bounds for general circuits [30], nearly cubic lower bounds for formula size [23], nearly n log log n size lower bounds for branching programs [12], n1+cd for depth d threshold circuits [26]). Here, we present two instances where pathetic lower bounds of the form n1+e would suffice to derandomize interesting classes of probabilistic algorithms. We show: - If the word problem over S5 requires constant-depth threshold circuits of size n1+e for some e > 0, then any language accepted by uniform polynomialsize probabilistic threshold circuits can be solved in subexponential time (and more strongly, can be accepted by a uniform family of deterministic constant-depth threshold circuits of subexponential size.) - If no constant-depth arithmetic circuits of size n1+e can multiply a sequence of n 3-by-3 matrices, then for every constant d, black-box identity testing for depth-d arithmetic circuits with bounded individual degree can be performed in subexponential time (and even by a uniform family of deterministic constant-depth AC0 circuits of subexponential size)." @default.
- W2397366471 created "2016-06-24" @default.
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- W2397366471 date "2010-01-01" @default.
- W2397366471 modified "2023-09-22" @default.
- W2397366471 title "Uniform Derandomization from Pathetic Lower Bounds." @default.
- W2397366471 hasPublicationYear "2010" @default.
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