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Volume 28, No 3, 2021, P. 90-103 UDC 519.716+519.214.7
Keywords: three-valued logic, random variable, distribution, approximation. DOI: 10.33048/daio.2021.28.707 Aleksey D. Yashunsky 1 Received February 24, 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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