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Pseudorandom sources for BPP

Jack H. Lutz
1990 Journal of computer and system sciences (Print)  
Almost every sequence in DSPACE (2 r"iynomia') is a source for every BPP-machine. %  ...  The following results are proven: For every BPPmachine M, almost every sequence in DSPACE (2a"car ) is a source for M. Every pspacerandom sequence is a source for every BPP-machine.  ...  Levin for helpful discussions  ... 
doi:10.1016/0022-0000(90)90023-e fatcat:5tzfouscyjfmnmutpmkhbh4p54

DERANDOMIZATION: A BRIEF OVERVIEW [chapter]

VALENTINE KABANETS
2004 Current Trends in Theoretical Computer Science  
Acknowledgments I want to thank Lance Fortnow, Oded Goldreich, Russell Impagliazzo, Dieter van Melkebeek, Chris Umans, Salil Vadhan, and Avi Wigderson for a number of helpful comments and suggestions that  ...  But, the existence of such pseudorandom generators would imply much more than the derandomization of BPP.  ...  The correctness proof of such extractor constructions relies upon a "decoding" procedure for strings x sampled from a source of weak randomness.  ... 
doi:10.1142/9789812562494_0012 fatcat:znfvduwgrjexpcbcj62ientmvy

Page 4540 of Mathematical Reviews Vol. , Issue 91H [page]

1991 Mathematical Reviews  
Dekhtyar (Tver) 91h:68086 68Q30 68Q15 Lutz, Jack H. (1-IASU-C) Pseudorandom sources for BPP. J. Comput. System Sci. 41 (1990), no. 3, 307-320.  ...  The following results are proven: For every BPP- machine M, almost every sequence in DSPACE(2!"**") is a source for M. Every pspace-random sequence is a source for every BPP- machine.  ... 

Randomness vs Time: Derandomization under a Uniform Assumption

Russell Impagliazzo, Avi Wigderson
2001 Journal of computer and system sciences (Print)  
ACKNOWLEDGMENT We are greatful to the referee for many valuable comments.  ...  A BPP algorithm that had a markedly different behavior using a pseudorandom sequence as its source of randomness than using a truly random sequence would be such an adversary.  ...  (Note that, to construct the adversary from the BPP algorithm, an input for which the pseudorandom generator fails must be found.  ... 
doi:10.1006/jcss.2001.1780 fatcat:iqrss6b62vcrxmqd2mbii3oxcu

Pseudorandom Generators [chapter]

Oded Goldreich
1999 Modern Cryptography, Probabilistic Proofs and Pseudorandomness  
Suppose that for all m there exists an (m, 1/8) pseudorandom generator G : Proof.  ...  Let A(x; r) be a BPP algorithm that on inputs x of length n, can be simulated by Boolean circuits of size at most most n c , using coin tosses r.  ...  randomized algorithm; and • Simulating BPP with any weak random source.  ... 
doi:10.1007/978-3-662-12521-2_3 fatcat:d44aduuufjgijhehp4toyijjz4

Pseudorandom Generators [chapter]

Evangelos Kranakis
1986 Primality and Cryptography  
Suppose that for all m there exists an (m, 1/8) pseudorandom generator G : Proof.  ...  Let A(x; r) be a BPP algorithm that on inputs x of length n, can be simulated by Boolean circuits of size at most most n c , using coin tosses r.  ...  randomized algorithm; and • Simulating BPP with any weak random source.  ... 
doi:10.1007/978-3-322-96647-6_4 fatcat:6febgpanvrfpbbihvvwqsn77zq

Pseudorandomness

Salil P. Vadhan
2012 Foundations and Trends® in Theoretical Computer Science  
The structure of the presentation is meant to be suitable for teaching in a graduate-level course, with exercises accompanying each section. 2 1.  ...  graphs, randomness extractors, list-decodable error-correcting codes, samplers, and pseudorandom generators.  ...  I am indebted to Oded, Shafi, Madhu, Avi, Luca, and Omer for all the insights and research experiences they have shared with me.  ... 
doi:10.1561/0400000010 fatcat:2xv2ssm7lbhnjktg6l3u5o5kfu

Pseudorandomness and Average-Case Complexity Via Uniform Reductions

Luca Trevisan, Salil Vadhan
2007 Computational Complexity  
Impagliazzo and Wigderson (36th FOCS, 1998) gave the first construction of pseudorandom generators from a uniform complexity assumption on EXP (namely EXP = BPP).  ...  -PseudoTIME(n 2k · 2 t −1 (n) ) for every constant k. Let t (n) = t(n) 2k . Then for any constant c, t (t (n c )) ≤ t(t(n c )) for a constant c , because t is a nice time bound.  ...  is a (k, )-extractor if, for every k-source X, E(X, U d ) is -close to U m .  ... 
doi:10.1007/s00037-007-0233-x fatcat:zx5jlgq5argtpnqw3vf2nhgqwm

Noise optimizes super-Turing computation in recurrent neural networks

Emmett Redd, Steven Senger, Tayo Obafemi-Ajayi
2021 Physical Review Research  
The exponents maximize to the accepted values for the logistic and Hénon maps when the noise equals eight times the least significant bit of the noisy recurrent signals for the logistic digital RNN and  ...  An analog RNN with those limits calculates at the super-Turing complexity level BPP/log*.  ...  For any natural number m, we have that P BPP/ log (m) *.  ... 
doi:10.1103/physrevresearch.3.013120 fatcat:k7q2x4olgvafvkcvgtnhphrsre

In search of an easy witness: exponential time vs. probabilistic polynomial time

Russell Impagliazzo, Valentine Kabanets, Avi Wigderson
2002 Journal of computer and system sciences (Print)  
We also prove several downward closure results for ZPP, RP, BPP, and MA; e.g., we show EXP ¼ BPP3EE ¼ BPE, where EE is the double-exponential time class and BPE is the exponential-time analogue of BPP:  ...  In particular, we show that NEXPCP=poly3NEXP ¼ MA; this can be interpreted as saying that no derandomization of MA (and, hence, of promise-BPP) is possible unless NEXP contains a hard Boolean function.  ...  Acknowledgments The authors would like to thank Lance Fortnow, Dieter van Melkebeek, and Salil Vadhan for their comments; special thanks are due to Dieter van Melkebeek for pointing out an error in an  ... 
doi:10.1016/s0022-0000(02)00024-7 fatcat:lvshl4tmdrbnlaqly4ejcoarri

A Novel Grouping Genetic Algorithm for the One-Dimensional Bin Packing Problem on GPU [chapter]

Sukru Ozer Ozcan, Tansel Dokeroglu, Ahmet Cosar, Adnan Yazici
2016 Communications in Computer and Information Science  
Large problem instances of the 1D-BPP cannot be solved exactly due to the intractable nature of the problem.  ...  One-dimensional Bin Packing Problem (1D-BPP) is a challenging NP-Hard combinatorial problem which is used to pack finite number of items into minimum number of bins.  ...  heuristics to obtain high quality solutions for large scale 1D-BPP instances.  ... 
doi:10.1007/978-3-319-47217-1_6 fatcat:anyzz4jzirdldef5lttvsnr7oq

Normal numbers and sources for BPP

Martin Strauss
1997 Theoretical Computer Science  
Lutz also trades some universality for abundance, showing that for any one machine, almost all sequences in ESPACE = DSPACE(2*i"eX) are, for all inputs, sources. *  ...  In [lo], Lutz proposed a notion of source, a nonrandom sequence that can substitute in a certain way for the random bits used by bounded-error probabilistic machines.  ...  that the sources for BPP, as defined, are exactly the normal numbers, and so there is a source in AC'.  ... 
doi:10.1016/s0304-3975(96)00099-0 fatcat:5ssiztysajcc5pdd2irlnjluj4

Unexpected Power of Random Strings

Shuichi Hirahara, Michael Wagner
2020 Innovations in Theoretical Computer Science  
a nonadaptive polynomial-time algorithm is to derandomize BPP."  ...  It was conjectured by Allender (CiE 2012 [1] ) and others that their lower bound is tight when a reduction works for every universal Turing machine; i.e., "the only way to make use of random strings by  ...  Any query of length O(log n) should be useful only as a source of "pseudorandomness" [3] .  ... 
doi:10.4230/lipics.itcs.2020.41 dblp:conf/innovations/Hirahara20 fatcat:piztb2rwvbcvxh3mhpsljgubsy

Sparse pseudorandom distributions

Oded Goldreich, Hugo Krawczyk
1992 Random structures & algorithms (Print)  
Clearly, the uniform distribution is a pseudorandom one. But do such trivial cases exhaust the notion of pseudorandomness?  ...  In this paper we investigate the existence of pseudorandom distributions, using no unproven assumptions. We show that sparse pseudorandom distributions do exist.  ...  ACKNOWLEDGEMENTS We would like to thank Micha Hofri for referring us to Hoeffding inequality, and to Benny Chor and Eyal Kushilevitz for helpful comments.  ... 
doi:10.1002/rsa.3240030206 fatcat:cfywwwbbr5as5mcm7fm2lvai7y

On Statistically Secure Obfuscation with Approximate Correctness [chapter]

Zvika Brakerski, Christina Brzuska, Nils Fleischhacker
2016 Lecture Notes in Computer Science  
We overcome this barrier by using a PRF as a "baseline" for the obfuscated program. We broaden our study and consider relaxed notions of security for iO.  ...  Technically, previous approaches utilized the behavior of the obfuscator on evasive functions, for which saiO always exists.  ...  Acknowledgments We are grateful to Andrej Bogdanov, Kai-Min Chung, Siyao Guo, Markulf Kohlweiss, Arno Mittelbach and Vinod Vaikuntanathan for helpful discussions.  ... 
doi:10.1007/978-3-662-53008-5_19 fatcat:6wk5snn5wrgfpogc5mbs4lo7ky
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