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154
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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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
Comparing Notions of Full Derandomization
 In Proceedings of the Sixteenth Annual IEEE Conference on Computational Complexity
, 2001
"... Most of the hypotheses of full derandomization fall into two sets of equivalent statements: Those equivalent to the existence of ecient pseudorandom generators and those equivalent to approximating the accepting probability of a circuit. We give the rst relativized world where these sets of equiv ..."
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Cited by 15 (0 self)
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of equivalent statements are not equivalent to each other. 1 Introduction Impagliazzo and Wigderson [IW97] show that if there exists a language E that requires 2 n) size circuits then P = BPP. Andreev, Clementi and Rolim [ACR98] show that if ecient hitting set generators exist then P = BPP. A careful look
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 ..."
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Cited by 5 (2 self)
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seed length even when given a function which is hard for relatively small circuits. Generators with optimal seed length were previously known only assuming hardness for exponential size circuits [IW97, STV01]. We also give the first explicit construction of an extractor which uses asymptotically
Extractors and Pseudorandom generators using the hard core lemma
, 2010
"... We present a construction of an extractor based exclusively on hardness amplification which extracts from sources with (some) polynomially small minentropy. This improves upon a similar construction of the author with Trevisan ([DT09]) both in terms of the entropy rate and seed length. The extracto ..."
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is the first in literature which does not use ReedMuller code or the NisanWigderson generator. Perhaps more interestingly, every bit in the output of the pseudorandom generator requires computing f at roughly N β2 positions. Previous pseudorandom generators (from worst case hardness) in [IW97, STV01, SU05
Norms, XOR lemmas, and lower bounds for GF(2) polynomials and multiparty protocols
 In Proceedings of the 22nd Annual Conference on Computational Complexity. IEEE
, 2007
"... This paper presents a unified and simple treatment of basic questions concerning two computational models: multiparty communication complexity and GF (2) polynomials. The key is the use of (known) norms on Boolean functions, which capture their proximity to each of these models (and are closely rela ..."
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Cited by 23 (6 self)
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�. • For cbit kparty protocols we obtain a bound of 2 −Ω(m) in the special case when ɛ ≤ exp � −c · 2 k �. In this range of ɛ, our bound improves on a direct product lemma for twoparties by Parnafes, Raz, and Wigderson (STOC ’97). We also use the norms to give improved (or just simplified) lower bounds
Averagecase Complexity, and Error Correcting Codes. Direct Product Theorems are more formal statements with
, 2009
"... the following general intuition: “if there is a problem which is hard to solve on the average, then solving multiple instances of the problem becomes even harder.” Such theorems are useful in the following settings: (i) Cryptography: Much of Cryptography is based on existence of problems which are h ..."
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to distinguish between the two. (ii) Derandomization: A series of results (e.g. [NW94, IW97]) show a very interesting HardnessvsRandomness tradeoff. These results show the following sequence of implications: if there is a function which is hard in the worstcase, then there exists a function which is mildly
Department of Computer Science,
"... We consider uniform assumptions for derandomization. We provide intuitive evidence that BPP can be simulated nontrivially in deterministic time by showing that (1) There is a simulation of P in P OLY LOGSP ACE that is successful against all polynomialtime adversaries infinitely often, or BP P ⊆ SU ..."
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⊆ SUBEXP (2) There is a simulation of P in SUBP SP ACE that is successful against all polynomialtime adversaries infinitely often, or BP P = P. These results complement and extend earlier work of Sipser, NisanWigderson and Lu. We show similar tradeoffs between simulation of nondeterministic time
On Efficient Constructions of Short Lists Containing Mostly Ramsey Graphs
"... One of the earliest and bestknown application of the probabilistic method is the proof of existence of a 2 log nRamsey graph, i.e., a graph with n nodes that contains no clique or independent set of size 2 log n. The explicit construction of such a graph is a major open problem. We show that a rea ..."
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One of the earliest and bestknown application of the probabilistic method is the proof of existence of a 2 log nRamsey graph, i.e., a graph with n nodes that contains no clique or independent set of size 2 log n. The explicit construction of such a graph is a major open problem. We show that a reasonable hardness assumption implies that in polynomial time one can construct a list containing polylog(n) graphs such that most of them are 2 log nRamsey.
Results 1  10
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154