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Diskretnaya Matematika, 2014, Volume 26, Issue 4, Pages 43–50
DOI: https://doi.org/10.4213/dm1303
(Mi dm1303)
 

This article is cited in 11 scientific papers (total in 11 papers)

Images of subset of finite set under iterations of random mappings

A. M. Zubkov, A. A. Serov

Steklov Mathematical Institute of Russian Academy of Sciences
References:
Abstract: Let N be a set of N elements and F1,F2, be a sequence of random independent equiprobable mappings NN. For a subset S0N,|S0|=n, we consider a sequence of its images Sk=Fk(F2(F1(S0))),k=1,2, and a sequence of their unions Ψk=S1Sk,k=1,2  An approach to the exact computation of distribution of |Sk| and |Ψk| for moderate values of N is described. Two-sided inequalities for M|Sk| and M|Ψk| such that upper bound are asymptotically equivalent to lower ones for N,n,k,nk=o(N) are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.
Keywords: iterations of random mappings, time-memory tradeoff algorithm.
Received: 20.06.2014
English version:
Discrete Mathematics and Applications, 2015, Volume 25, Issue 3, Pages 179–185
DOI: https://doi.org/10.1515/dma-2015-0017
Bibliographic databases:
Document Type: Article
UDC: 519.212.2+519.213.21
Language: Russian
Citation: A. M. Zubkov, A. A. Serov, “Images of subset of finite set under iterations of random mappings”, Diskr. Mat., 26:4 (2014), 43–50; Discrete Math. Appl., 25:3 (2015), 179–185
Citation in format AMSBIB
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\paper Images of subset of finite set under iterations of random mappings
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\pages 43--50
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Linking options:
  • https://www.mathnet.ru/eng/dm1303
  • https://doi.org/10.4213/dm1303
  • https://www.mathnet.ru/eng/dm/v26/i4/p43
  • This publication is cited in the following 11 articles:
    1. Benjamin Allen, Alex McAvoy, “The coalescent in finite populations with arbitrary, fixed structure”, Theoretical Population Biology, 158 (2024), 150  crossref
    2. V. O. Mironkin, “Sloi v grafe k-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, Matem. vopr. kriptogr., 10:1 (2019), 73–82  mathnet  crossref  elib
    3. V. O. Mironkin, “Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping”, Discrete Math. Appl., 31:4 (2021), 259–269  mathnet  crossref  crossref  mathscinet  isi  elib
    4. V. O. Mironkin, “Raspredelenie dliny otrezka aperiodichnosti v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 10:3 (2019), 89–99  mathnet  crossref
    5. A. M. Zubkov, A. A. Serov, “Estimates of the mean size of the subset image under composition of random mappings”, Discrete Math. Appl., 28:5 (2018), 331–338  mathnet  crossref  crossref  mathscinet  isi  elib
    6. V. O. Mironkin, V. G. Mikhailov, “O mnozhestve obrazov k-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, Matem. vopr. kriptogr., 9:3 (2018), 99–108  mathnet  crossref  elib
    7. V. O. Mironkin, “Ob otsenkakh raspredeleniya dliny otrezka aperiodichnosti v grafe k-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, PDM, 2018, no. 42, 6–17  mathnet  crossref  elib
    8. A. M. Zubkov, A. A. Serov, “Limit theorem for the size of an image of subset under compositions of random mappings”, Discrete Math. Appl., 28:2 (2018), 131–138  mathnet  crossref  crossref  mathscinet  isi  elib
    9. A. M. Zubkov, V. O. Mironkin, “Raspredelenie dliny otrezka aperiodichnosti v grafe k-kratnoi iteratsii sluchainogo ravnoveroyatnogo otobrazheniya”, Matem. vopr. kriptogr., 8:4 (2017), 63–74  mathnet  crossref  mathscinet  elib
    10. Kogan D., Manohar N., Boneh D., “T/Key: Second-Factor Authentication From Secure Hash Chains”, Ccs'17: Proceedings of the 2017 Acm Sigsac Conference on Computer and Communications Security, Assoc Computing Machinery, 2017, 983–999  crossref  isi  scopus
    11. A. A. Serov, “Images of a finite set under iterations of two random dependent mappings”, Discrete Math. Appl., 26:3 (2016), 175–181  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
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