On some properties of finitely generating transformer sets for $p$-ary fractions
Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 4, pp. 124-135.

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We study expressibility of rational probabilities under transformations of random variables with distributions from some initial set by Boolean functions. We investigate finite generation of probabilities expressed by $p$-ary fractions for prime $p$ not less than $5$. We prove some properties that Boolean functions from a finitely generating set should have. Bibliogr. 11.
Mots-clés : Bernoulli random variable, random variable transformation.
Keywords: finite generation
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E. E. Trifonova. On some properties of finitely generating transformer sets for $p$-ary fractions. Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 4, pp. 124-135. http://geodesic.mathdoc.fr/item/DA_2022_29_4_a6/

[1] A. D. Yashunsky, “Algebras of probability distributions on finite sets”, Proc. Steklov Inst. Math., 301 (2018), 304–318 | DOI | MR

[2] R. L. Skhirtladze, “On synthesis of $p$-schemes using switches with random discrete states”, Soobshchen. Akad. Nauk Gruz. SSR, 26:2 (1961), 181–186 (in Russian)

[3] R. L. Skhirtladze, Modeling of random variables by logic algebra functions, Cand. Sci. Diss., Izd. Tbil. Univ., Tbilisi, 1966 (in Russian)

[4] F. I. Salimov, “The question of simulation of Boolean random variables by means of logic algebra functions”, Probabilistic Methods and Cybernetics, 15, Izd. Kazan. Univ., Kazan, 1979, 68–89 (Russian)

[5] F. I. Salimov, “On a system of generators for algebras over random variables”, Sov. Math., 25:5 (1981), 92–97 | MR

[6] F. I. Salimov, “A family of distribution algebras”, Sov. Math., 32:7 (1988), 106–118 | MR

[7] R. M. Kolpakov, “On generation of some classes of rational numbers by probabilistic $\pi$-nets”, Mosc. Univ. Math. Bull., 46:2 (1991), 27–29 | MR

[8] R. M. Kolpakov, “On the bounds for the complexity of generation of rational numbers by stochastic contact $\pi$-networks”, Mosc. Univ. Math. Bull., 47:6 (1992), 34–36 | MR

[9] R. M. Kolpakov, “On the generation of rational numbers by probabilistic contact nets”, Mosc. Univ. Math. Bull., 47:5 (1992), 41–46 | MR

[10] R. M. Kolpakov, “On the generation of rational numbers by monotone functions”, Theoretical and Applied Aspects of Mathematical Research, Izd. Mosk. Univ., M., 1994, 13–17 (in 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, 2021, no. 1, 39–48 (in Russian)