Skip to main content
SpringerLink
Log in

Multiplicative Properties of Spectral Walsh Coefficients of the Boolean Function

  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

It is shown for the first time that spectral Walsh coefficients of the Boolean function have the structure in the form of the product of Walsh derivatives of this function. A method and an algorithm are suggested for the analysis of multiplicative properties of Walsh coefficients in terms of the behavior of the Boolean function and results of the experiments on test logic circuits are 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. Akers, S.B., On a Theory of Boolean Functions, SIAM J., 1959, vol. 7, no.4, pp. 487-498.

    Google Scholar 

  2. Edwards, C.R., The Gibbs Dyadic Differentiator and Its Relationship to the Boolean Difference, Comput. Electron. Eng., 1978, vol. 5, no.4, pp. 335-344.

    Google Scholar 

  3. Toshich, Zh., Arifmeticheskie predstavleniya logicheskikh funktsii. Diskretnye avtomaty i seti svyazi (Arithmetic Representations of Logic Functions. Discrete Automata and Communication Networks), Moscow: Nauka, 1970.

    Google Scholar 

  4. Shmerko, V.P., Synthesis of the Arithmetic Forms of Boolean Functions by Means of the Fourier Transform, Avtom. Telemekh., 1989, no. 5, pp. 134-142.

    Google Scholar 

  5. Yanushkevich, S.N., Development of Methods of the Boolean Differential Calculus for the Arithmetic Logic, Avtom. Telemekh., 1994, no. 5, pp. 121-137.

    Google Scholar 

  6. Yanushkevich, S.N., Systolic Algorithms of Synthesis of Arithmetic Polynomial Forms of the k-Valued Functions of the Boolean Algebra, Avtom. Telemekh., 1994, no. 12, pp. 128-142.

    Google Scholar 

  7. Jankovic, D., Stankovic, R., and Drechsler, R., Decision Diagram Method for Calculation of Pruned Walsh Transform, IEEE Trans. Comput., 2001, vol. 50, no.2, pp. 147-157.

    Google Scholar 

  8. Sadykhov, P.Kh., Chegolin, P.M., and Shmerko, V.P., Obrabotka signalov v diskretenykh bazisakh (Processing of Signals in Discrete Bases), Minsk: Nauka i Tekhnika, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Calgary University, Calgary, Canada

    C. N. Yanushkevich

Authors
  1. C. N. Yanushkevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yanushkevich, C.N. Multiplicative Properties of Spectral Walsh Coefficients of the Boolean Function. Automation and Remote Control 64, 1938–1947 (2003). https://doi.org/10.1023/B:AURC.0000008432.39581.c1

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:AURC.0000008432.39581.c1

Keywords

Search

Navigation