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Derandomizing from Random Strings
"... In this paper we show that BPP is truthtable reducible to the set of Kolmogorov random strings RK. It was previously known that PSPACE, and hence BPP is Turingreducible to RK. The earlier proof relied on the adaptivity of the Turingreduction to find a Kolmogorovrandom string of polynomial length ..."
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Cited by 9 (2 self)
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In this paper we show that BPP is truthtable reducible to the set of Kolmogorov random strings RK. It was previously known that PSPACE, and hence BPP is Turingreducible to RK. The earlier proof relied on the adaptivity of the Turingreduction to find a Kolmogorovrandom string of polynomial length
Convolution Kernels on Discrete Structures
, 1999
"... We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes the fa ..."
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Cited by 506 (0 self)
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We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes
On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
 In STOC
, 2005
"... Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear co ..."
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Cited by 364 (6 self)
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Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear
Derandomization via complexity theory
"... Noam Nisan constructed pseudo random number generators which convert O(S log R) truly random bits to R bits that appear random to any algorithm that runs in SP ACE(S). 2 D Sivakumar, demonstrated that a large class of probabilistic algorithms can be derandomized using Nisan’s construction. 1 This cl ..."
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This class of algorithms is characterized by the fact that each probabilistic algorithm can thought of as a set of log space bounded tests being performed on random bit strings drawn from a uniform distribution. A detailed description of the method and this class of algorithms is presented. 1.
Randomness vs. Time: Derandomization under a uniform assumption
"... We prove that if BPP � = EXP, then every problem in BPP can be solved deterministically in subexponential time on almost every input ( on every samplable ensemble for infinitely many input sizes). This is the first derandomization result for BP P based on uniform, noncryptographic hardness assumptio ..."
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Cited by 72 (11 self)
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is identical to that used in the analogous nonuniform results of [21, 3]. However, previous proofs of correctness assume the “hard function ” is not in P/poly. They give a nonconstructive argument that a circuit distinguishing the pseudorandom strings from truly random strings implies that a similarly
Natural Proofs Versus Derandomization
"... We study connections between Natural Proofs, derandomization, and the problem of proving “weak” circuit lower bounds such as NEXP ⊂ TC 0, which are still wide open. Natural Proofs have three properties: they are constructive (an efficient algorithm A is embedded in them), have largeness (A accepts ..."
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Cited by 4 (1 self)
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. • There are no Pnatural properties useful against C if and only if randomized exponential time can be “derandomized ” using truth tables of circuits from C as random seeds. Therefore the task of proving there are no Pnatural properties is inherently a derandomization problem, weaker than but implied
Hardness vs. randomness
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1994
"... We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE,...) using an arbitrary function tha ..."
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Cited by 298 (27 self)
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We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE,...) using an arbitrary function
Lecture SpaceBounded Derandomization
"... We now discuss derandomization of spacebounded algorithms. Here nontrivial results can be shown without making any unproven assumptions, in contrast to what is currently known for derandomizing timebounded algorithms. We show first that1 BPL ⊆ SPACE(log 2 n) and then improve the analysis and show ..."
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= 2 O(S) possible configurations of Mx, and there is an edge from a to b labeled by the string r ∈ {0, 1} ℓ if and only if Mx moves from configuration a to configuration b after reading r as its next ℓ random bits. Computation of Mx is then equivalent to a random walk of length R/ℓ on this graph
Lecture TimeBounded Derandomization
"... Randomization can (provably) provide benefits in many settings; examples include cryptography (where random keys are used to provide protection against an adversary) and distributed computing (where randomness can be used as a means to break symmetry between parties). Randomness also appears to help ..."
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to help in algorithm design. But is it possible that, from a complexitytheoretic perspective, randomness does not help? E.g., might it be the case that every problem that can be solved in randomized polynomial time can also be solved in deterministic polynomial time? (That is, is P = BPP?) Historically
Derandomization in cryptography
 SIAM J. COMPUTING
"... We give two applications of Nisan–Wigdersontype (“noncryptographic”) pseudorandom generators in cryptography. Specifically, assuming the existence of an appropriate NWtype generator, we construct: 1. A onemessage witnessindistinguishable proof system for every language in NP, based on any trapd ..."
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Cited by 23 (4 self)
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trapdoor permutation. This proof system does not assume a shared random string or any setup assumption, so it is actually an “NP proof system.” 2. A noninteractive bit commitment scheme based on any oneway function. The specific NWtype generator we need is a hitting set generator fooling nondeterministic
Results 1  10
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