Skip to main content
SpringerLink
Log in

On Classes of Superfunctions on Two-Element Set

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

Superfunctions, i.e., sets of Boolean functions dependent on the same variables are considered. The closure operation is defined on the set of superfunctions. The issues of completeness and expressibility are studied for this functional system.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. E. L. Post, ‘‘Introduction to a general theory of elementary propositions’’, Amer. J. Math. 43 (3) 163–185 (1921).

    Article  MathSciNet  Google Scholar 

  2. E. L. Post, The Two-Valued Iterative Systems of Mathematical Logic, Annals of Mathematics Studies, vol. 6 (Princeton Univ. Press, Princeton, 1941). https://doi.org/10.1515/9781400882366

  3. S. S. Marchenkov and A. B. Ugol’nikov, Closed Classes of Boolean Functions (Inst. Prikladnoi Matematiki Keldysha, Moscow, 1990).

    MATH  Google Scholar 

  4. S. S. Marchenkov Foundations of the Theory of Boolean Functions (Fizmatlit, Moscow, 2014).

    Google Scholar 

  5. V. V. Tarasov, ‘‘Completeness criterion for incompletely defined functions of Boolean algebra’’, Probl. Kibern., No. 30, pp. 319–325 (1975).

  6. H. Machida, ‘‘Hyperclones on a two-element set’’, Multiple Valued Logic: Int. J. 8, 495–501 (2002).

    Article  MathSciNet  Google Scholar 

  7. J. Čolić Oravec, H. Machida, J. Pantović, and G. Vojvodić, ‘‘From clones to hyperclones’’, Zb. Rad. Sel. Top. Logic Comput. Sci. 18 (26), 111–144 (2015).

    MathSciNet  Google Scholar 

Download references

ACKNOWLEDGMENTS

The author thanks O.S. Dudakova for problem formulation and discussion of the results of this work.

Funding

The work is supported by the Russian Foundation for Basic Research (project no. 18-01-00337) and by the Russian Science Foundation (project no. 19-71-30004).

Author information

Authors and Affiliations

  1. Chair of Discrete Mathematics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    I. I. Maslova

Authors
  1. I. I. Maslova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. I. Maslova.

Ethics declarations

The author declares that she has no conflicts of interest.

Additional information

Translated by E. Oborin

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maslova, I.I. On Classes of Superfunctions on Two-Element Set. Moscow Univ. Math. Bull. 76, 234–238 (2021). https://doi.org/10.3103/S0027132221050041

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132221050041

Keywords:

Search

Navigation