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Derandomizing from Random Strings [article]

Harry Buhrman and Lance Fortnow and Michal Koucký and Bruno Loff
2009 arXiv   pre-print
The earlier proof relied on the adaptivity of the Turing-reduction to find a Kolmogorov-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 .  ... 
arXiv:0912.3162v1 fatcat:u3omgcizevfdrige55uyvq2fh4

Derandomizing from Random Strings

Harry Buhrman, Lance Fortnow, Michal Koucký, Bruno Loff
2010 2010 IEEE 25th Annual Conference on Computational Complexity  
The earlier proof relied on the adaptivity of the Turingreduction to find a Kolmogorov-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 .  ... 
doi:10.1109/ccc.2010.15 dblp:conf/coco/BuhrmanFKL10 fatcat:bphxoqbwjjatfladjnrqglesuy

DERANDOMIZATION: A BRIEF OVERVIEW [chapter]

VALENTINE KABANETS
2004 Current Trends in Theoretical Computer Science  
This survey focuses on the recent (1998)(1999)(2000)(2001)(2002)(2003) developments in the area of 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  ... 
doi:10.1142/9789812562494_0012 fatcat:znfvduwgrjexpcbcj62ientmvy

Pseudorandom Generators and Typically-Correct Derandomization [chapter]

Jeff Kinne, Dieter van Melkebeek, Ronen Shaltiel
2009 Lecture Notes in Computer Science  
The area of 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.  ... 
doi:10.1007/978-3-642-03685-9_43 fatcat:ymn7xluqcbgpdoanbbt76pshie

Derandomizing Arthur-Merlin Games under Uniform Assumptions [chapter]

Chi-Jen Lu
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 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.  ... 
doi:10.1007/3-540-40996-3_26 fatcat:3r7bguaabbaulbhe6ergxkdnt4

Derandomizing Arthur--Merlin games under uniform assumptions

C.-J. Lu
2001 Computational Complexity  
We study how the nondeterminism versus determinism problem and the time versus space problem are related to the problem of 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.  ... 
doi:10.1007/s00037-001-8196-9 fatcat:xa7tuxxpxjfhldmbbrk3hils34

Infeasibility of instance compression and succinct PCPs for NP

Lance Fortnow, Rahul Santhanam
2011 Journal of computer and system sciences (Print)  
To this end, we introduce a new strong 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.  ... 
doi:10.1016/j.jcss.2010.06.007 fatcat:nh4jffjefzemzoizvhmdpxrjse

Efficient estimation of Pauli observables by derandomization [article]

Hsin-Yuan Huang, Richard Kueng, John Preskill
2021 arXiv   pre-print
Starting with 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.  ... 
arXiv:2103.07510v1 fatcat:5zjttcmxhzag5lq6w2mharv6pe

Typically-correct derandomization

Ronen Shaltiel
2010 ACM SIGACT News  
A fundamental question in complexity theory is whether every 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.  ... 
doi:10.1145/1814370.1814389 fatcat:unfdkttcq5arrixtomcacrgq2u

Infeasibility of instance compression and succinct PCPs for NP

Lance Fortnow, Rahul Santhanam
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
To this end, we introduce a new strong 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.  ... 
doi:10.1145/1374376.1374398 dblp:conf/stoc/FortnowS08 fatcat:tur4jkqnr5cjzcwyw3weqr6lbi

On derandomization and average-case complexity of monotone functions

George Karakostas, Jeff Kinne, Dieter van Melkebeek
2012 Theoretical Computer Science  
We show that, in fact, any 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.  ... 
doi:10.1016/j.tcs.2012.02.017 fatcat:6mk5ovihtzaxvhrexnd2vt5tci

In a World of P=BPP [chapter]

Oded Goldreich
2011 Lecture Notes in Computer Science  
canonical 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.  ... 
doi:10.1007/978-3-642-22670-0_20 fatcat:ha5wfxp2y5cz7ju6sygvp65oui

Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size [article]

V. Arvind, Partha Mukhopadhyay
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.  ... 
arXiv:0804.0957v2 fatcat:6wnwcgo6jfbcjcqwaxc4txiory

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

Jeff Kinne, Dieter van Melkebeek, Ronen Shaltiel
2011 Computational Complexity  
The area of 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  ... 
doi:10.1007/s00037-011-0019-z fatcat:6w32whkz7bahfkrxjko2klxgli

Hardness as randomness: a survey of universal derandomization [article]

Russell Impagliazzo
2003 arXiv   pre-print
from random.  ...  Hardness from derandomization Are circuit lower bounds necessary for derandomization?  ... 
arXiv:cs/0304040v1 fatcat:vp2asft6sbcxvom7jwth43me7e
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