Skip to main content
SpringerLink
Log in

Information Content of the Ternary Decision Diagrams

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

Abstract

Information content of the ternary decision diagrams (EXOR-TDD) was discussed from the standpoint of spectral transform. Since the EXOR-TDDs are defined in an extended (redundant) basis, its information content is much greater than that of other decision diagrams. To construct the EXOR-TDD for a given function f, the Boolean derivatives of all possible orders were determined with respect to all variables of f. Therefore, different AND-EXOR decision diagrams are contained in the EXOR-TDDs as individual subtrees. Since each of the subtrees is an AND-EXOR expression for f, a procedure was proposed to determine the coefficient of these expressions by analyzing the paths in the EXOR-TDD. The logical Gibbs derivatives also were shown to be obtainable from the EXOR-TDDs.

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. Kurepa, Dj.R., Ensembles ordonnés et ramifiés, Paris: Thése, 1935.

    Google Scholar 

  2. Kurepa, Dj.R., Sets–Logics–Machines, Proc. Int. Symp. Theory of Switching, Cambridge: Harvard Univ., 1957, part 1, pp. 137–146.

    Google Scholar 

  3. Stanković, R.S. and Sasao, T., Decision Diagrams for Discrete Functions: Classification and Unified Interpretation, Proc. Asian and South Pacific Design Automation Conf. ASP-DAC'98, Yokohama, Japan, 1998, pp. 439–446.

  4. Stanković, R.S., Some Remarks about Spectral Transform Interpretation of MTBDDs and EVBDDs, ASP-DAC'95, Chiba, Japan, 1995, pp. 385–390.

  5. Stanković, R.S., Spectral Transform Decision Diagrams in Simple Questions and Simple Answers, Belgrade: Nauka, 1998.

    Google Scholar 

  6. Stanković, R.S. and Sasao, T., Spectral Interpretation of TDDs, SASIMI'97, pp. 45–50.

  7. Stanković, R.S., Sasao, T., and Moraga, C., Spectral Transform Decision Diagrams, in Sasao, T. and Fujita, M. Representations of Discrete Functions, Boston: Kluwer, 1996, pp. 55–92.

    Google Scholar 

  8. Sasao, T., Ternary Decision Diagrams and Their Applications, ISMVL-97, 1997, pp. 241–250.

  9. Akers, S.B., Binary Decision Diagrams, IEEE Trans. Comput., 1978, vol. C-27, no. 6, pp. 509–516.

    Google Scholar 

  10. Bryant, R.E., Graph-based Algorithms for Boolean Functions Manipulation, IEEE Trans. Comput., 1986, vol. C-35, no. 8, pp. 667–691.

    Google Scholar 

  11. Drechsler, R. and Becker, B., OKFDDs-Algorithms, Applications and Extensions, in Sasao, T. and Fujita, M. Representations of Discrete Functions, Boston: Kluwer, 1996, pp. 163–190.

    Google Scholar 

  12. Sasao, T. and Fujita, M., Representations of Discrete Functions, Boston: Kluwer, 1996.

    Google Scholar 

  13. Sasao, T., Representations of Logic Functions by Using Exor Operators, in Sasao, T. and Fujita, M. Representations of Discrete Functions, Boston: Kluwer, 1996, pp. 29–54.

    Google Scholar 

  14. Sasao, T., Ternary Decision Diagrams and Their Applications, in Sasao, T. and Fujita, M. Representations of Discrete Functions, Boston: Kluwer, 1996, pp. 269–292.

    Google Scholar 

  15. Stanković, R.S., Gibbs Derivatives, Numer. Funct. Anal. Optimiz., 1994, vol. 15, no. 1–2, pp. 169–181.

    Google Scholar 

  16. Gibbs, J.E., Walsh Spectrometry: A Form of Spectral Analysis Well Suited to Binary Digital Computation, NPL DES Rept., Teddington, Middlesex, England, 1967.

  17. Butzer, P.L. and Stanković, R.S., Theory and Applications of Gibbs Derivatives, Beograd: Matematički Inst., 1990.

    Google Scholar 

  18. Hurst, S.L., The Logical Processing of Digital Signals, New York: Crane, Russak, 1978.

    Google Scholar 

  19. Su Weiyi., Gibbs Derivatives and Their Applications, Rept. Inst. Math., Nanjing University, 91–7, Nanjing, P.R. China, 1991, pp. 1–20.

  20. Yanushkevich, S.N., Logic Differential Calculus in Multi-Valued Logic Design, Szczecin: Tech. Univ. of Szczecin Academic Publ., 1998.

    Google Scholar 

  21. Edwards, C.R., The Gibbs Dyadic Differentiator and Its Relationship to the Boolean Difference, Comput. Elect. Eng., 1978, vol. 5, pp. 335–344.

    Google Scholar 

  22. Edwards, C.R., The Design of Easily Tested Circuits Using Mapping and Symmetry Methods, Radio Electron. Engr., 1977, vol. 47, pp. 321–342.

    Google Scholar 

  23. Edwards, C.R., The Generalized Dyadic Differentiator and Its Application to 2–Valued Functions Defined on an N-Space, Proc. IEE Comput. Digit. Techn., 1978, vol. 1, no. 4, pp. 137–142.

    Google Scholar 

  24. Sasao, T., Logic Synthesis and Optimization, Boston: Kluwer, 1993.

    Google Scholar 

  25. Stanković, R.S., Matrix-valued EXOR-TDDs in Decomposition of Switching Functions, ISMVL'99, Freiburg-im-Bereisgau, Germany, 1999.

  26. Sasao, T., FPGA Design by Generalized Functional Decomposition, Boston: Kluwer, 1993, pp. 233–258.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Niš, Niš, Yugoslavia

    R. S. Stanković

Authors
  1. R. S. Stanković
    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

Stanković, R.S. Information Content of the Ternary Decision Diagrams. Automation and Remote Control 63, 666–679 (2002). https://doi.org/10.1023/A:1015138417389

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015138417389

Keywords

Search

Navigation