Skip to main content
Log in

On Some Properties of Finitely Generating Transformer Sets for \(p\)-ary Fractions

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

We study the 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 possess.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

REFERENCES

  1. A. D. Yashunsky, “Algebras of probability distributions on finite sets,” Tr. MIAN 301 (), 320–335 (2018) [Proc. Steklov Inst. Math. 301 , 304–318 (2018)].

    Article  MathSciNet  MATH  Google Scholar 

  2. R. L. Skhirtladze, “On synthesis of \( p \)-schemes using switches with random discrete states,” Soobshch. Akad. Nauk Gruz. SSR 26 (2), 181–186 (1961).

    MathSciNet  Google Scholar 

  3. R. L. Skhirtladze, “Modeling of random variables by logic algebra functions,” Cand. Sci. (Phys.-Math.) Dissertation (Izd. Tbilis. Univ., Tbilisi, 1966) [in Russian].

  4. F. I. Salimov, “The question of simulation of Boolean random variables by means of logic algebra functions,” in Probabilistic Methods and Cybernetics (Izd. Kazan. Univ., Kazan, 1979), no. 15, 68–89 [in Russian].

  5. F. I. Salimov, “On a system of generators for algebras over random variables,” Izv. Vyssh. Uchebn. Zaved. Mat. (5), 78–82 (1981) [Sov. Math. 25 (5), 92–97 (1981)].

    MathSciNet  MATH  Google Scholar 

  6. F. I. Salimov, “A family of distribution algebras,” Izv. Vyssh. Uchebn. Zaved. Mat. (7), 64–72 (1988) [Sov. Math. 32 (7), 106–118 (1988)].

    MathSciNet  MATH  Google Scholar 

  7. R. M. Kolpakov, “On generation of some classes of rational numbers by probabilistic \( \pi \)-nets,” Vestn. Mosk. Univ. Ser. 1. Mat. Mekh. (2), 27–30 (1991) [Moscow Univ. Math. Bull. 46 (2), 27–29 (1991)].

    MathSciNet  MATH  Google Scholar 

  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. (6), 62–65 (1992) [Moscow Univ. Math. Bull. 47 (6), 34–36 (1992)].

    MathSciNet  MATH  Google Scholar 

  9. R. M. Kolpakov, “On the generation of rational numbers by probabilistic contact nets,” Vestn. Mosk. Univ. Ser. 1. Mat. Mekh. (5), 46–52 (1992) [Moscow Univ. Math. Bull. 47 (5), 41–46 (1992)].

    MathSciNet  MATH  Google Scholar 

  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), 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 (1), 39–48 (2021).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. E. Trifonova.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Trifonova, E.E. On Some Properties of Finitely Generating Transformer Sets for \(p\)-ary Fractions. J. Appl. Ind. Math. 16, 834–840 (2022). https://doi.org/10.1134/S1990478922040226

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478922040226

Keywords

Navigation