Filters








949 Hits in 3.3 sec

Pseudorandom generators for combinatorial shapes

Parikshit Gopalan, Raghu Meka, Omer Reingold, David Zuckerman
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
We construct 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.  ... 
doi:10.1145/1993636.1993671 dblp:conf/stoc/GopalanMRZ11 fatcat:ettvowd5qrbjtnfv3hwb3fc7ou

Pseudorandom generators for combinatorial checkerboards

Thomas Watson
2012 Computational Complexity  
We consider the problem of constructing explicit 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.  ... 
doi:10.1007/s00037-012-0036-6 fatcat:7nakuya3zvhmpfrczey5jp5clm

Pseudorandom Generators for Combinatorial Checkerboards

Thomas Watson
2011 2011 IEEE 26th Annual Conference on Computational Complexity  
We consider the problem of constructing explicit 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.  ... 
doi:10.1109/ccc.2011.12 dblp:conf/coco/Watson11 fatcat:w2u4wiyjuvg2dl74mg237mxvbq

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*/?  ... 

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.  ... 

PhD Abstracts

GRAHAM HUTTON
2015 Journal of functional programming  
In addition, we discovered that the 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.  ... 
doi:10.1017/s0956796815000167 fatcat:6t25jkfshjfdtj7hv5mxmjcwfm

Defect Level Estimation for Pseudorandom Testing Using Stochastic Analysis

W. B. Jone, D. C. Huang, S. C. Chang, S. R. Das
2001 VLSI design (Print)  
Although the defect level estimation 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.  ... 
doi:10.1155/2001/28741 fatcat:4v7vkxy6nvcmvbtootel5bvn4q

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.  ... 

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  ... 

Optimal Hitting Sets for Combinatorial Shapes [article]

Aditya Bhaskara, Devendra Desai, Srikanth Srinivasan
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.  ... 
arXiv:1211.3439v1 fatcat:yhqvdqd5avaqdastqr6hedmd3m

Fourier Bounds and Pseudorandom Generators for Product Tests

Chin Ho Lee, Michael Wagner
2019 Computational Complexity Conference  
Our 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.  ... 
doi:10.4230/lipics.ccc.2019.7 dblp:conf/coco/Lee19 fatcat:dyl6htns7jhw7pfrjbgdkobhha

Stream cipher based on pseudorandom number generation with optical affine transformation

Toru Sasaki, Hiroyuki Togo, Jun Tanida, Yoshiki Ichioka
2000 Applied Optics  
The stream cipher uses a 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.  ... 
doi:10.1364/ao.39.002340 pmid:18345143 fatcat:rzxbveyp7nct3atv5exqidmtsi

Book announcements

1994 Discrete Applied Mathematics  
Dimension in discrete spaces. mathematical theory of 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.  ... 
doi:10.1016/0166-218x(94)90074-4 fatcat:ud3msi2a4fgtlokdrhzy3ieh7m

Optimal Hitting Sets for Combinatorial Shapes [chapter]

Aditya Bhaskara, Devendra Desai, Srikanth Srinivasan
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  ... 
doi:10.1007/978-3-642-32512-0_36 fatcat:mh3cuhkikzantnqmudcyibfkve

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

Parikshit Gopalan, Amir Yehudayoff
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 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.  ... 
arXiv:1402.3543v2 fatcat:ulzvvmbolfgovfvvmqhyqu36oi
« Previous Showing results 1 — 15 out of 949 results