Skip to main content
SpringerLink
Log in

Complexity and Structure of Circuits for Parity Functions

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

The paper is devoted to circuits implementing parity functions. A review of results establishing exact values of the complexity of parity functions is given. The structure of optimal circuits implementing parity functions is described for some bases. For one infinite basis, an upper bound for the complexity of parity functions is given.

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. Yu. A. Kombarov, “On minimal realizations of linear Boolean functions,” Diskret. Anal. Issled. Oper., 19, No. 3, 39–57 (2012).

    MathSciNet  MATH  Google Scholar 

  2. Yu. A. Kombarov, “On minimal circuits in Sheffer basis for linear Boolean functions,” Diskret. Anal. Issled. Oper., 20, No. 4, 65–87 (2013).

    MathSciNet  MATH  Google Scholar 

  3. H. Ch. Lai and S. Muroga, “Logic networks with a minimum number of NOR (NAND) gates for parity functions of n variables,” IEEE Trans. Comput., C-36, No. 2, 157–166 (1987).

  4. O. Podolskaya, On Circuit Complexity of Parity and Majority Functions in Antichain Basis, http: //arxiv.org/abs/1410.2456.

  5. N. P. Redkin, “Proof of minimality of circuits consisting of functional elements,” Systems Theor. Research, 23, 85–103 (1973).

    Article  Google Scholar 

  6. N. P. Redkin, “On minimal realization of linear function by circuits of functional elements,” Kibernetika, 6, 31–38 (1971).

    MathSciNet  Google Scholar 

  7. I. S. Shkrebela, “On the complexity of the realization of linear Boolean functions by circuits of functional elements over the basis \( \left\{x\to y,\overline{x}\right\} \) ,” Diskret. Mat., 15, No. 4, 100–112 (2003).

  8. I. Wegner, “The complexity of the parity function in unbounded fan-in, unbounded depth circuits,” Theor. Comput. Sci., 85, 155–170 (1991).

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    Yu. A. Kombarov

Authors
  1. Yu. A. Kombarov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. A. Kombarov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 20, No. 6, pp. 147–153, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kombarov, Y.A. Complexity and Structure of Circuits for Parity Functions. J Math Sci 233, 95–99 (2018). https://doi.org/10.1007/s10958-018-3926-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-018-3926-6

Search

Navigation