Skip to main content
SpringerLink
Log in

On the length of a read-many certificate in certain extended elementary bases

  • Published:
Moscow University Computational Mathematics and Cybernetics Aims and scope Submit manuscript

Abstract

The following problem is considered: find a couple of sets (a certificate) with which we can verify if the functions of n variables in a given basis are read-once functions. This work obtains the logarithmic lower bound estimates of the Shannon function of certificate length for all functions of n variables in bases consisting of conjunction, disjunction, negation, and one of Stecenko monotone functions. It is thus shown that the elementary basis is the only one for which read-many certificate length is bound by a constant.

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. A. A. Voronenko, “On the Shannon function for read-many certificate length in one base family,” Moscow Univ. Comput. Math. Cybernet. 37, 26–27 (2013).

    Article  MATH  MathSciNet  Google Scholar 

  2. C. E. Shannon, “A Symbolic Analysis of Relay and Switching Circuits,” AIEE Trans. 57, 713–723 (1938).

    Google Scholar 

  3. V. A. Stetsenko, “On prepoor bases in P2,” Mat. Vopr. Kibern., No. 4, 139–177 (1992).

    Google Scholar 

  4. A. A. Voronenko, V. S. Fedorova, and D. V. Chistikov, “Repeatability of Boolean functions in an elementary basis,” Russ. Math., No. 11, 61–65 (2011).

    Google Scholar 

  5. D. Chistikov, V. Fedorova, and A. Voronenko, “Certificates of non-membership for classes of read-once functions,” Fundam. Inform., No. 1, 63–77 (2014).

    Google Scholar 

  6. I. K. Sharankhaev, “On nonrepeated Boolean functions in pre-elementary monotonous bases,” Diskret. Mat. 21, 2 (2009).

    Google Scholar 

  7. I. K. Sharankhaev, “On Boolean bases of the second tier,” Izv. Vyssh. Uchebn. Zaved., Mat. No. 3, 81–82 (2004).

    Google Scholar 

  8. I. K. Sharankhaev, “On weakly repeated Boolean functions in a pre-elementary basis,” Diskret. Analiz Issled. Operats., Ser. 1., 10(2), 79–101 (2003).

    MATH  MathSciNet  Google Scholar 

  9. A. A. Voronenko, “On complexity of the proof of repeatability of Boolean functions in a binary basis,” Prikl. Mat. Inform. (Mosk. Gos. Univ.), No. 3(13), 12–16 (2011).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    D. V. Kaftan

Authors
  1. D. V. Kaftan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. V. Kaftan.

Additional information

Original Russian Text © D.V. Kaftan, 2015, published in Vestnik Moskovskogo Universiteta. Vychislitel’naya Matematika i Kibernetika, 2015, No. 2, pp. 40–46.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaftan, D.V. On the length of a read-many certificate in certain extended elementary bases. MoscowUniv.Comput.Math.Cybern. 39, 88–95 (2015). https://doi.org/10.3103/S0278641915020041

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0278641915020041

Keywords

Search

Navigation