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Pseudorandom generators for combinatorial shapes

2011
*
Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11
*

We construct

doi:10.1145/1993636.1993671
dblp:conf/stoc/GopalanMRZ11
fatcat:ettvowd5qrbjtnfv3hwb3fc7ou
*pseudorandom**generators**for**combinatorial**shapes*, which substantially*generalize**combinatorial*rectangles, -biased spaces, 0/1 halfspaces, and 0/1 modular sums. ...*Combinatorial**shapes**generalize**combinatorial*rectangles, halfspaces with 0/1 coefficients, and modular sums. ... We now derandomize the*generator*of Theorem 5.9 to get our main result*for*fooling*combinatorial**shapes*. Proof of Theorem 1.3. ...##
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Pseudorandom generators for combinatorial checkerboards

2012
*
Computational Complexity
*

We consider the problem of constructing explicit

doi:10.1007/s00037-012-0036-6
fatcat:7nakuya3zvhmpfrczey5jp5clm
*pseudorandom**generators**for**combinatorial*checkerboards. This is a*generalization*of small-bias*generators*, which correspond to the case m = 2. ... We construct a*pseudorandom**generator*that ǫ-fools all*combinatorial*checkerboards with seed length O log m + log d · log log d + log 3/2 1 ǫ . ... Acknowledgments I thank Siu Man Chan, Siu On Chan, Anindya De, and Luca Trevisan*for*helpful discussions, and I thank anonymous referees*for*helpful comments. ...##
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Pseudorandom Generators for Combinatorial Checkerboards

2011
*
2011 IEEE 26th Annual Conference on Computational Complexity
*

We consider the problem of constructing explicit

doi:10.1109/ccc.2011.12
dblp:conf/coco/Watson11
fatcat:w2u4wiyjuvg2dl74mg237mxvbq
*pseudorandom**generators**for**combinatorial*checkerboards. This is a*generalization*of small-bias*generators*, which correspond to the case m = 2. ... We construct a*pseudorandom**generator*that ǫ-fools all*combinatorial*checkerboards with seed length O log m + log d · log log d + log 3/2 1 ǫ . ... Acknowledgments I thank Siu Man Chan, Siu On Chan, Anindya De, and Luca Trevisan*for*helpful discussions. ...##
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Page 1462 of Mathematical Reviews Vol. , Issue 2000b
[page]

2000
*
Mathematical Reviews
*

*generators*

*for*

*combinatorial*rectangles. ... Summary: “We explicitly construct a

*pseudorandom*

*generator*which uses O(logm + logd + log*/? ...

##
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Page 1571 of Mathematical Reviews Vol. , Issue 84d
[page]

1984
*
Mathematical Reviews
*

Dieter [same journal 12 (1974), 223-246; MR 52
#15949] which

*generates*random gamma variates with*shape*parameter less than unity. ... J. 84d:65004 A note on gamma variate*generators*with*shape*parameter less than unity. (German summary) Computing 30 (1983), no. 2, 185-188. ...##
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PhD Abstracts

2015
*
Journal of functional programming
*

In addition, we discovered that the

doi:10.1017/s0956796815000167
fatcat:6t25jkfshjfdtj7hv5mxmjcwfm
*pseudorandom*number*generator*used by us*for*random testing is unreliable, and that no reliable contruction exists that supports our particular requirements. ... Random Structured Test Data*Generation**for*Black-Box Testing M I C H A L H. ...##
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Defect Level Estimation for Pseudorandom Testing Using Stochastic Analysis

2001
*
VLSI design (Print)
*

Although the defect level estimation

doi:10.1155/2001/28741
fatcat:4v7vkxy6nvcmvbtootel5bvn4q
*for**pseudorandom*testing has been performed using sequential statical analysis, no closed form can be accomplished as complex*combinatorial*enumerations are involved ... Results demonstrate that the defect level analysis*for**pseudorandom*testing by only dealing with the worst single stuck-at fault is not adequate (In fact, the worst single stuck-at fault analysis is just ... The diculty of deriving a closed form*for*the DL equation lies in the involvement of very complex*combinatorial*enumerations. ...##
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Page 5203 of Mathematical Reviews Vol. , Issue 89I
[page]

1989
*
Mathematical Reviews
*

Mach. 33 (1986), no. 4, 792-807; MR 88d:68044] in- troduced the notion of a

*pseudorandom*function*generator*and showed how to construct a*pseudorandom*function*generator*from a*pseudorandom*bit*generator*... A preliminary Section | gives an ab- stract syntax*for*strings and tree-*shaped*terms. ...##
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Page 5185 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
*
Mathematical Reviews
*

It is known that if the trails are required to be all of the same

*shape*, then this works only*for*m= 3, 5 and 7 [D. E. Bryant and C. C. ... The paper is motivated by the following problem that arises in the study of quadratic*pseudorandom*number*generators*modulo a composite integer: given M, {a a} C {2,3,4...} find all odd m € M such that ...##
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Optimal Hitting Sets for Combinatorial Shapes
[article]

2012
*
arXiv
*
pre-print

*Generalizing*results of Linial, Luby, Saks, and Zuckerman (Combinatorica 1997) and Rabani and Shpilka (SICOMP 2010), we construct hitting sets

*for*

*Combinatorial*

*Shapes*of size polynomial in the alphabet ... We consider the problem of constructing explicit Hitting sets

*for*

*Combinatorial*

*Shapes*, a class of statistical tests first studied by Gopalan, Meka, Reingold, and Zuckerman (STOC 2011). ... Definition 2.2 (

*Pseudorandom*

*Generators*and Hitting Sets). Let F ⊆ {0, 1} D denote a boolean function family

*for*some input domain D. ...

##
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Fourier Bounds and Pseudorandom Generators for Product Tests

2019
*
Computational Complexity Conference
*

Our

doi:10.4230/lipics.ccc.2019.7
dblp:conf/coco/Lee19
fatcat:dyl6htns7jhw7pfrjbgdkobhha
*generator*in particular works*for*the well-studied class of*combinatorial*rectangles, where in addition we allow the bits to be read in any order. ... As a result, we construct*pseudorandom**generators**for*such functions with seed length Õ(m + log(k/ε)), which is optimal up to polynomial factors in log m, log log k and log log(1/ε). ... However, the*generator*in [33] works even when the f i have range C ≤1 , which implies*generators**for*several variants of product tests such as*generalized*halfspaces and*combinatorial**shapes*. ...##
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Stream cipher based on pseudorandom number generation with optical affine transformation

2000
*
Applied Optics
*

The stream cipher uses a

doi:10.1364/ao.39.002340
pmid:18345143
fatcat:rzxbveyp7nct3atv5exqidmtsi
*pseudorandom*number*generator*͑PRNG͒ to*generate*a*pseudorandom*bit sequence. ... We propose a new, to our knowledge, stream cipher technique*for*two-dimensional ͑2-D͒ image data that can be implemented by iterative optical transformation. ... The random bit sequence, which is used as a key*for*encryption, is*generated*by a*pseudorandom*number*generator*͑PRNG͒. ...##
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Book announcements

1994
*
Discrete Applied Mathematics
*

Dimension in discrete spaces. mathematical theory of

doi:10.1016/0166-218x(94)90074-4
fatcat:ud3msi2a4fgtlokdrhzy3ieh7m
*shape*(The notion of*shape*. The notion of*shape**for*very irregular spaces.*Shape*invariants, operations, and properties. ... Finite topological spaces: The*general*topological discussion). ... Ensembles of genetic regulatory systems:*Generic*properties. Implications*for*ontogeny. Cell types as a*combinatorial*epigenetic code. Summary. ...##
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Optimal Hitting Sets for Combinatorial Shapes
[chapter]

2012
*
Lecture Notes in Computer Science
*

*Generalizing*results of Linial, Luby, Saks, and Zuckerman (Combinatorica 1997) and Rabani and Shpilka (SICOMP 2010), we construct explicit hitting sets

*for*

*combinatorial*

*shapes*of size polynomial in the ... We consider the problem of constructing explicit Hitting Sets

*for*

*combinatorial*

*shapes*, a class of statistical tests first studied by Gopalan, Meka, Reingold, and Zuckerman (STOC 2011). ... Acknowledgements The authors are very grateful to the anonymous referees

*for*correcting various errors and deficiencies in an earlier version of the paper and also simplifying some of the notation and ...

##
###
Inequalities and tail bounds for elementary symmetric polynomial with applications
[article]

2015
*
arXiv
*
pre-print

We use this to give a simpler and more modular analysis of a construction of min-wise independent hash functions and

arXiv:1402.3543v2
fatcat:ulzvvmbolfgovfvvmqhyqu36oi
*pseudorandom**generators**for**combinatorial*rectangles due to Gopalan et al., which also ... We show that if |S_k(x)|,|S_k+1(x)| are small relative to |S_k-1(x)|*for*some k>0 then |S_ℓ(x)| is also small*for*all ℓ > k. ... We thank an anonymous referee*for*pointing out an error in the statement of Theorem 4 in a previous version of the paper. ...
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