Skip to main content
Log in

Completeness of systems of functions for classes of extended superposition

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

The problem of realization of Boolean functions by formulas of special type is considered. The notion of the supplement of systems of Boolean functions is defined. Criteria of completeness of the considered functional systems are obtained.

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.

Similar content being viewed by others

References

  1. Ya, V, Akulov, “Criteria of Completeness for Classes of Extended Superposition,” in Proc. X Int. Workshop “Discrete Mathematics and its Applications,” MSU, Moscow, February 1–6, 2010 (Moscow State Univ., Mech. Math. Dept., Moscow, 2010), pp. 167–169.

    Google Scholar 

  2. E. L. Post, “Introduction to a General Theory of Elementary Propositions,” Amer. J. Math. 43(3), 163 (1921).

    Article  MATH  MathSciNet  Google Scholar 

  3. E. L. Post, Two-Valued Iterative Systems of Mathematical Logic. Ann. Math. Stud. Vol. 5 (Princeton Univ. Press, Princeton, 1941).

    Google Scholar 

  4. S. V. Yablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Functions of the Algebra of Logic and Post Classes (Nauka, Moscow, 1966) [in Russian].

    Google Scholar 

  5. A. B. Ugol’nikov, Post Classes (Moscow Univ., Mech. Math. Dept., Moscow, 2008) [in Russian].

    Google Scholar 

  6. A. B. Ugol’nikov, “Closed Post Classes,” Izv. Vuzov, Matem. No. 7, 79 (1988).

  7. Yu. I. Yanov and A. A. Muchnik, “Existence of k-Valued Closed Classes Having no Finite Bases,” Doklady Akad. Nauk SSSR 127(1), 44 (1959).

    MATH  Google Scholar 

  8. O. S. Tarasova, “Classes of Functions of Three-Valued Logic Closed with Respect to Operations of Superposition and Permutation,” Matem. Voprosy Kibern. 13, 59 (2004).

    MATH  MathSciNet  Google Scholar 

  9. S. V. Yablonskii, Introduction to Discrete Mathematics (Vysshaya Shkola, Moscow, 2006) [in Russian].

    Google Scholar 

  10. S. V. Yablonskii, “A Family of Classes of Functions of Algebra of Logic Admitting Simple Circuit Implementation,” Uspekhi Matem. Nauk 12, 139 (1957).

    MathSciNet  Google Scholar 

  11. S. V. Yablonskii, “Algorithmic Difficulties of the Synthesis of Minimal Contact Circuits,” in Problemy Kibernetiki (Fizmatgiz, Moscow, 1969), Vol. 2, pp. 75–121 [in Russian].

    Google Scholar 

  12. Yu. V. Kuznetsov, “Classes of Boolean Functions Invariant with Respect to Identification of Variables,” Doklady Akad. Nauk SSSR 290(4), 780 (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © Ya.V. Akulov, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 1, pp. 36–41.

About this article

Cite this article

Akulov, Y.V. Completeness of systems of functions for classes of extended superposition. Moscow Univ. Math. Bull. 66, 35–40 (2011). https://doi.org/10.3103/S0027132211010074

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132211010074

Keywords

Navigation