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762
Pseudorandom generators without the XOR Lemma (Extended Abstract)
, 1998
"... Impagliazzo and Wigderson [IW97] have recently shown that if there exists a decision problem solvable in time 2 O(n) and having circuit complexity 2 n) (for all but finitely many n) then P = BPP. This result is a culmination of a series of works showing connections between the existence of har ..."
Abstract

Cited by 137 (23 self)
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with the Nisan Wigderson [NW94] generator. In this paper we present two different approaches to proving the main result of Impagliazzo and Wigderson. In developing each approach, we introduce new techniques and prove new results that could be useful in future improvements and/or applications of hardness
Reducing the seed length in the NisanWigderson generator
 COMBINATORICA
, 2006
"... The NisanWigderson pseudorandom generator [NW94] was constructed to derandomize probabilistic algorithms under the assumption that there exist explicit functions which are hard for small circuits. We give the first explicit construction of a pseudorandom generator with asymptotically optimal seed ..."
Abstract

Cited by 5 (2 self)
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The NisanWigderson pseudorandom generator [NW94] was constructed to derandomize probabilistic algorithms under the assumption that there exist explicit functions which are hard for small circuits. We give the first explicit construction of a pseudorandom generator with asymptotically optimal
On the proof complexity of the NisanWigderson generator based on a hard NP ∩ coNP function
"... ..."
How strong is Nisan’s pseudorandom generator?
, 2010
"... We study the resilience of the classical pseudorandom generator (PRG) of Nisan [Nis92] against spacebounded machines that make multiple passes over the input. Our motivation comes from the derandomization of BPNC1. Observe that if for every logspace machine that reads its input nO(1) times there ..."
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We study the resilience of the classical pseudorandom generator (PRG) of Nisan [Nis92] against spacebounded machines that make multiple passes over the input. Our motivation comes from the derandomization of BPNC1. Observe that if for every logspace machine that reads its input nO(1) times
Hardness vs. Randomness Result by Nisan and Widgerson
"... This is a write up of results of Nisan and Wigderson [1] along the lines of “if hard problems exist then randomized algorithms can be derandomized.” We DEFINE many terms, STATE how they relate, and then PROVE that that is how they relate. We parameterize everything and then later set the parameters ..."
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This is a write up of results of Nisan and Wigderson [1] along the lines of “if hard problems exist then randomized algorithms can be derandomized.” We DEFINE many terms, STATE how they relate, and then PROVE that that is how they relate. We parameterize everything and then later set the parameters
Lower Bounds for OBDDs and Nisan's pseudorandom generator
"... We present a new boolean function for which any Ordered Binary Decision Diagram (OBDD) computing it has an exponential number of nodes. This boolean function is obtained from Nisan's pseudorandom generator to derandomize space bounded randomized algorithms. Though the relation between hardne ..."
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We present a new boolean function for which any Ordered Binary Decision Diagram (OBDD) computing it has an exponential number of nodes. This boolean function is obtained from Nisan's pseudorandom generator to derandomize space bounded randomized algorithms. Though the relation between
Results 1  10
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762