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Volume 28, No 3, 2021, P. 90-103

UDC 519.716+519.214.7
A. D. Yashunsky
On three-valued random variable transformations by bivariate functions

Abstract:
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, distribution, approximation.

DOI: 10.33048/daio.2021.28.707

Aleksey D. Yashunsky 1
1. Keldysh Institute of Applied Mathematics RAS,
4 Miusskaya Square, 125047 Moscow, Russia
e-mail: yashunsky@keldysh.ru

Received February 24, 2021
Revised February 24, 2021
Accepted March 18, 2021

References

[1] R. G. Bukharaev, On controlled generators of random numbers, in Probabilistic Methods and Cybernetics. II (Uch. Zap. Kazan. Gos. Univ., Vol. 123, B. 6) (Izd. Kazan. Univ., Kazan, 1963), pp. 68–87 [Russian].

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

[3] S. Markovski, Design of crypto primitives based on quasigroups, Quasigr. Relat. Syst. 23 (1), 41–90 (2015).

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

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

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

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

[8] A. D. Yashunsky, Algebras of probability distributions on finite sets, Tr. Mat. Inst. Steklov. 301, 320–335 (2018) [Russian] [Proc. Steklov Inst. Math. 301, 305–319 (2018)].

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

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

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