Abstract:
Let N be a set of N elements and F1,F2,… be a sequence of random independent equiprobable mappings N→N. For a subset S0⊂N,|S0|=n, we consider a sequence of its images Sk=Fk(…F2(F1(S0))…),k=1,2…, and a sequence of their unions Ψk=S1∪…∪Sk,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.
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
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\paper Images of subset of finite set under iterations of random mappings
\jour Diskr. Mat.
\yr 2014
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\issue 4
\pages 43--50
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\jour Discrete Math. Appl.
\yr 2015
\vol 25
\issue 3
\pages 179--185
\crossref{https://doi.org/10.1515/dma-2015-0017}
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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
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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
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