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Volume 29, No 4, 2022, P. 124-135 UDC 519.7
Keywords: Bernoulli random variable, finite generation, random variable transformation. DOI: 10.33048/daio.2022.29.731 Ekaterina E. Trifonova 1 Received January 25, 2022 References[1] A. D. Yashunsky, Algebras of probability distributions on finite sets, Tr. MIAN 301, 320–335 (2018) [Russian] [Proc. Steklov Inst. Math. 301, 304–318 (2018)].[2] R. L. Skhirtladze, On synthesis of $p$-schemes using switches with random discrete states, Soobshchen. Akad. Nauk Gruz. SSR 26 (2), 181–186 (1961) [Russian]. [3] R. L. Skhirtladze, Modeling of random variables by logic algebra functions, Cand. Sci. Diss. (Izd. Tbil. Univ., Tbilisi, 1966) [Russian]. [4] F. I. Salimov, The question of simulation of Boolean random variables by means of logic algebra functions, in Probabilistic Methods and Cybernetics, No. 15 (Izd. Kazan. Univ., Kazan, 1979), pp. 68–89 [Russian]. [5] F. I. Salimov, On a system of generators for algebras over random variables, Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 78–82 (1981) [Russian] [Sov. Math. 25 (5), 92–97 (1981)]. [6] F. I. Salimov, A family of distribution algebras, Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 64–72 (1988) [Russian] [Sov. Math. 32 (7), 106–118 (1988)]. English version: Journal of Applied and Industrial Mathematics 16 (4) (2022). [7] R. M. Kolpakov, On generation of some classes of rational numbers by probabilistic $\pi$-nets, Vestn. Mosk. Univ., Ser. 1. Mat. Mekh., No. 2, 27–30 (1991) [Russian] [Mosc. Univ. Math. Bull. 46 (2), 27–29 (1991)]. [8] R. M. Kolpakov, On the bounds for the complexity of generation of rational numbers by stochastic contact $\pi$-networks, Vestn. Mosk. Univ., Ser. 1. Mat. Mekh., No. 6, 62–65 (1992) [Russian] [Mosc. Univ. Math. Bull. 47 (6), 34–36 (1992)]. [9] R. M. Kolpakov, On the generation of rational numbers by probabilistic contact nets, Vestn. Mosk. Univ., Ser. 1. Mat. Mekh., No. 5, 46–52 (1992) [Russian] [Mosc. Univ. Math. Bull 47 (5), 41–46 (1992)]. [10] R. M. Kolpakov, On the generation of rational numbers by monotone functions, in Theoretical and Applied Aspects of Mathematical Research (Izd. Mosk. Univ., Moscow, 1994), pp. 13–17 [Russian]. [11] E. E. Trifonova, On infinite generativeness of quinary fractions in a class of probability transformers. Izv. Vyssh. Uchebn. Zaved., Povolzh. Reg., Fiz.-Mat. Nauki, No. 1, 39–48 (2021) [Russian]. |
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