Geodesic
On three-valued random variable transformations by bivariate functions
Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 3, pp. 90-103.

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We consider transformations of three-valued random variables by three-valued logic functions. For arbitrary systems of bivariate functions that contain all functions with inessential variables we describe the classes of random variable distributions approximated by substituting independent random variables that omit at least one of three values for arguments of the said operations. Illustr. 2, bibliogr. 11.
Keywords: three-valued logic, random variable, approximation.
Mots-clés : distribution 
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A. D. Yashunsky. On three-valued random variable transformations by bivariate functions. Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 3, pp. 90-103. http://geodesic.mathdoc.fr/item/DA_2021_28_3_a4/

[1] R. G. Bukharaev, “On controlled generators of random numbers”, Probabilistic Methods and Cybernetics, v. II, Uch. Zap. Kazan. Gos. Univ., 123, no. 6, Izd. Kazan. Univ., Kazan, 1963, 68–87 (Russian)

[2] Wilhelm D., Bruck J., Qian L., “Probabilistic switching circuits in DNA”, Proc. Nat. Acad. Sci. USA, 115:5 (2018), 903–908

[3] Markovski S., “Design of crypto primitives based on quasigroups”, Quasigroups Related Syst., 23:1 (2015), 41–90 | Zbl

[4] R. M. Kolpakov, “Closed classes of finite distributions of rational probabilities”, Diskretn. Anal. Issled. Oper., Ser. 1, 11:3 (2004), 16–31 (Russian)

[5] R. L. Skhirtladze, “On a method for constructing a Boolean value with a given probability distribution”, Discrete Analysis, 7 (1966), 71–80 (Russian)

[6] A. D. Yashunsky, “On probability transformations by read-once Boolean formulas”, Proc. XVI Int. School and Seminar “Synthesis and Complexity of Control Systems” (St. Petersburg, Russia, June 26–30, 2006), Mekh.-Mat. Fak. MGU, M., 2006, 150–155 (Russian)

[7] Zhou H., Loh P.-L., Bruck J., The synthesis and analysis of stochastic switching circuits, Cornell Univ., Ithaca, NY, 2012, arXiv: 1209.0715

[8] A. D. Yashunsky, “Algebras of probability distributions on finite sets”, Proc. Steklov Inst. Math., 301 (2018), 305–319 | Zbl

[9] V. D. Belousov, Fundamentals of the Theory of Quasigroups and Loops, Nauka, M., 1967 (Russian)

[10] V. D. Belousov, “Nonassociative binary systems”, Algebra Topol. Geom. 1965, Itogi Nauki., Ser. Mat., VINITI, M., 1967, 63–81 (Russian)

[11] S. V. Yablonskii, “Functional constructions in a $k$-valued logic”, Trudy Mat. Inst. Steklov, 51, 1958, 5–142 (Russian)