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Diskr. Mat., 2018, Volume 30, Issue 2, Pages 27–36 (Mi dm1521)  

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

A. M. Zubkov, A. A. Serov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Let $\mathcal{X}_N$ be a set of $N$ elements and $F_1,F_2,\ldots$ be a sequence of random independent equiprobable mappings $\mathcal{X}_N\to\mathcal{X}_N$. For a subset $S_0\subset\mathcal{X}_N$, $|S_0|=m$, we consider a sequence of its images $S_t=F_t(\ldots F_2(F_1(S_0))\ldots)$, $t=1,2\ldots$ An approach to the exact recurrent computation of distribution of $|S_t|$ is described. Two-sided inequalities for $\mathbf{M}\{|S_t| | |S_0|=m\}$ such that the difference between the upper and lower bounds is $o(m)$ for $m,t,N\to\infty, mt=o(N)$ are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.

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

Funding Agency Grant Number
Russian Science Foundation 14-50-00005


DOI: https://doi.org/10.4213/dm1521

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English version:
Discrete Mathematics and Applications, 2018, 28:5, 331–338

Bibliographic databases:

Document Type: Article
UDC: 519.212.2
Received: 28.03.2018

Citation: A. M. Zubkov, A. A. Serov, “Estimates of the mean size of the subset image under composition of random mappings”, Diskr. Mat., 30:2 (2018), 27–36; Discrete Math. Appl., 28:5 (2018), 331–338

Citation in format AMSBIB
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