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Images of subset of finite set under iterations of random mappings
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Andrey M. Zubkov
and
Aleksandr A. Serov
Published/Copyright:
June 10, 2015
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.
Received: 2014-6-20
Published Online: 2015-6-10
Published in Print: 2015-6-1
© 2015 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Stationary distribution of the player rating in the Elo model with one adversary
- On the length of functions of κ-valued logic in the class of polynomial normal forms modulo κ
- Limit theorem for multitype critical branching process evolving in random environment
- An estimate of the approximation accuracy in B. A. Sevastyanov’s limit theorem and its application in the problem of random inclusions
- Investigation of the cryptosystem MST3 based on a Suzuki 2-group
- Images of subset of finite set under iterations of random mappings
