Abstract
AbstractLet XNbe a set ofNelements andF1,F2,… be a sequence of random independent equiprobable mappings XN→N. For a subsetS0⊂ XN, |S0|=m, we consider a sequence of its imagesSt=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 iso(m)form,t,N→ ∞,mt=o(N) are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.
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