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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

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CiteScore 2016: 0.16

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Volume 28, Issue 5

Issues

Estimates of the mean size of the subset image under composition of random mappings

Andrey M. Zubkov / Aleksandr A. Serov
Published Online: 2018-10-26 | DOI: https://doi.org/10.1515/dma-2018-0029

Abstract

Let XN be a set of N elements and F1, F2,… be a sequence of random independent equiprobable mappings XNN. For a subset S0 ⊂ XN, |S0|=m, we consider a sequence of its images St=Ft(…F2(F1(S0))…), t=1,2… An approach to the exact recurrent computation of distribution of |St| is described. Two-sided inequalities forM{|St|||S0|=m} such that the difference between the upper and lower bounds is o(m)for m, t, N → ∞, mt=o(N) are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.

Keywords: compositions of random mappings; time-memory tradeoff method

Note: Originally published in Diskretnaya Matematika (2018) 30, N2, 27–36 (in Russian).

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About the article

Received: 2018-03-28

Published Online: 2018-10-26

Published in Print: 2018-10-25


Communicated by Anatolij Dvurečenskij


Citation Information: Discrete Mathematics and Applications, Volume 28, Issue 5, Pages 331–338, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2018-0029.

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