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Derandomizing from Random Strings
[article]

2009
*
arXiv
*
pre-print

The earlier proof relied on the adaptivity of the Turing-reduction to find a Kolmogorov-

arXiv:0912.3162v1
fatcat:u3omgcizevfdrige55uyvq2fh4
*random**string*of polynomial length using the set R_K as oracle. ... In this paper we show that BPP is truth-table reducible to the set of Kolmogorov*random**strings*R_K. It was previously known that PSPACE, and hence BPP is Turing-reducible to R_K. ... In order to*derandomize*a BPP computation one needs a (pseudo)*random**string*of polynomial size. As mentioned before one can only obtain short, O(log n) sized,*random**strings**from*R K . ...##
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Derandomizing from Random Strings

2010
*
2010 IEEE 25th Annual Conference on Computational Complexity
*

The earlier proof relied on the adaptivity of the Turingreduction to find a Kolmogorov-

doi:10.1109/ccc.2010.15
dblp:conf/coco/BuhrmanFKL10
fatcat:bphxoqbwjjatfladjnrqglesuy
*random**string*of polynomial length using the set R K as oracle. ... In this paper we show that BPP is truth-table reducible to the set of Kolmogorov*random**strings*R K . It was previously known that PSPACE, and hence BPP is Turing-reducible to R K . ... In order to*derandomize*a BPP computation one needs a (pseudo)*random**string*of polynomial size. As mentioned before one can only obtain short, O(log n) sized,*random**strings**from*R K . ...##
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DERANDOMIZATION: A BRIEF OVERVIEW
[chapter]

2004
*
Current Trends in Theoretical Computer Science
*

This survey focuses on the recent (1998)(1999)(2000)(2001)(2002)(2003) developments in the area of

doi:10.1142/9789812562494_0012
fatcat:znfvduwgrjexpcbcj62ientmvy
*derandomization*, with the emphasis on the*derandomization*of time-bounded*randomized*complexity classes ... The correctness proof of such extractor constructions relies upon a "decoding" procedure for*strings*x sampled*from*a source of weak*randomness*. ... Recent developments*From*1998, the research on*derandomization*can be roughly divided into the following categories: 1. improvements of the hardness-*randomness*tradeoffs, 2. applications of the hardness-*randomness*...##
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Pseudorandom Generators and Typically-Correct Derandomization
[chapter]

2009
*
Lecture Notes in Computer Science
*

The area of

doi:10.1007/978-3-642-03685-9_43
fatcat:ymn7xluqcbgpdoanbbt76pshie
*derandomization*attempts to provide efficient deterministic simulations of*randomized*algorithms in various algorithmic settings. ... We show that our technique strictly generalizes an earlier approach by Shaltiel based on*randomness*extractors, and simplifies the proofs of some known results. ... Acknowledgments We would like to thank Oded Goldreich for suggesting the term "typically-correct*derandomization*," and Matt Anderson, Salil Vadhan, and anonymous reviewers for helpful comments. ...##
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Derandomizing Arthur-Merlin Games under Uniform Assumptions
[chapter]

2000
*
Lecture Notes in Computer Science
*

We study how the nondeterminism versus determinism problem and the time versus space problem are related to the problem of

doi:10.1007/3-540-40996-3_26
fatcat:3r7bguaabbaulbhe6ergxkdnt4
*derandomization*. ... This improves previous results and seems to be the first example of an interesting condition that implies three*derandomization*results at once. ... So to compute L, we guess |G|*strings*z 1 , . . . , z |G|*from*{0, 1} m , and accept x iff M (x, g i , z i ) = 1 for most i. ...##
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Derandomizing Arthur--Merlin games under uniform assumptions

2001
*
Computational Complexity
*

We study how the nondeterminism versus determinism problem and the time versus space problem are related to the problem of

doi:10.1007/s00037-001-8196-9
fatcat:xa7tuxxpxjfhldmbbrk3hils34
*derandomization*. ... This improves previous results and seems to be the first example of an interesting condition that implies three*derandomization*results at once. ... So to compute L, we guess |G|*strings*z 1 , . . . , z |G|*from*{0, 1} m , and accept x iff M (x, g i , z i ) = 1 for most i. ...##
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Infeasibility of instance compression and succinct PCPs for NP

2011
*
Journal of computer and system sciences (Print)
*

To this end, we introduce a new strong

doi:10.1016/j.jcss.2010.06.007
fatcat:nh4jffjefzemzoizvhmdpxrjse
*derandomization*hypothesis, the Oracle*Derandomization*Hypothesis, and discuss how it relates to traditional*derandomization*assumptions. ... (iii) An approach of Harnik and Naor to constructing collision-resistant hash functions*from*one-way functions is unlikely to be viable in its present form. ... choice of*random**string*. ...##
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Efficient estimation of Pauli observables by derandomization
[article]

2021
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arXiv
*
pre-print

Starting with

arXiv:2103.07510v1
fatcat:5zjttcmxhzag5lq6w2mharv6pe
*randomized*measurements, we propose an efficient*derandomization*procedure that iteratively replaces*random*single-qubit measurements with fixed Pauli measurements; the resulting deterministic ... In some cases, for example when some of the Pauli observables have a high weight, the*derandomized*procedure is substantially better than the*randomized*one. ... While the cost function is derived*from**derandomizing*the powerful*randomized*procedure [21] , it is not clear if this is the optimal cost function. ...##
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Typically-correct derandomization

2010
*
ACM SIGACT News
*

A fundamental question in complexity theory is whether every

doi:10.1145/1814370.1814389
fatcat:unfdkttcq5arrixtomcacrgq2u
*randomized*polynomial time algorithm can be simulated by a deterministic polynomial time algorithm (that is, whether BPP=P). ... A beautiful theory of*derandomization*was developed in recent years in attempt to solve this problem. ...*derandomization*on inputs that are feasibly generated arises naturally*from*the research on always-correct*derandomization*. ...##
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Infeasibility of instance compression and succinct PCPs for NP

2008
*
Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08
*

To this end, we introduce a new strong

doi:10.1145/1374376.1374398
dblp:conf/stoc/FortnowS08
fatcat:tur4jkqnr5cjzcwyw3weqr6lbi
*derandomization*hypothesis, the Oracle*Derandomization*Hypothesis, and discuss how it relates to traditional*derandomization*assumptions. * An earlier version of ... We show that there is no reduction*from*OR-SAT to any set A where the length of the output is bounded by a polynomial in n, unless NP ⊆ coNP/poly, and the Polynomial-Time Hierarchy collapses. ... choice of*random**string*. ...##
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On derandomization and average-case complexity of monotone functions

2012
*
Theoretical Computer Science
*

We show that, in fact, any

doi:10.1016/j.tcs.2012.02.017
fatcat:6mk5ovihtzaxvhrexnd2vt5tci
*derandomization*of*randomized*monotone computations would*derandomize*all*randomized*computations, whether monotone or not. ... We investigate whether circuit lower bounds for monotone circuits can be used to*derandomize**randomized*monotone circuits. ... Proof of Theorem 5 We follow the standard proof*from*the general setting and keep track of monotonicity to verify the final circuit is monotone or anti-monotone. ...##
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In a World of P=BPP
[chapter]

2011
*
Lecture Notes in Computer Science
*

canonical

doi:10.1007/978-3-642-22670-0_20
fatcat:ha5wfxp2y5cz7ju6sygvp65oui
*derandomizers*"). ... ., generators that suffice for such*derandomization*results). ... We assume that all polynomials, time bounds, and stretch functions are monotonically increasing functions*from*N to N, which means, in particular, that they are injective. ...##
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Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size
[article]

2008
*
arXiv
*
pre-print

*From*the result of Klivans-Spielman KS01 we observe that there is a

*randomized*polynomial-time identity test for commutative circuits of polynomial degree, also based on a more general isolation lemma ... We show that

*derandomizing*reasonably restricted versions of the isolation lemma implies circuit size lower bounds. ... We are grateful to Manindra Agrawal for interesting discussions and his suggestion that Theorem 5.2 can be obtained

*from*the stronger hypothesis. We also thank Srikanth Srinivasan for discussions. ...

##
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Pseudorandom Generators, Typically-Correct Derandomization, and Circuit Lower Bounds

2011
*
Computational Complexity
*

The area of

doi:10.1007/s00037-011-0019-z
fatcat:6w32whkz7bahfkrxjko2klxgli
*derandomization*attempts to provide efficient deterministic simulations of*randomized*algorithms in various algorithmic settings. ... In this paper we further the study of typically-correct*derandomization*in two ways. ... Acknowledgments We would like to thank Oded Goldreich for suggesting the term "typically-correct*derandomization*," and Matt Anderson, Valentine Kabanets, Salil Vadhan, and anonymous reviewers for helpful ...##
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Hardness as randomness: a survey of universal derandomization
[article]

2003
*
arXiv
*
pre-print

*from*

*random*. ... Hardness

*from*

*derandomization*Are circuit lower bounds necessary for

*derandomization*? ...

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