Skip to main content
Log in

Decomposition of underdetermined data

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

We consider the problem of the decomposition of an underdetermined source into a product of sources generating the symbols 0, 1, and the indefinite symbol *. We also study the problem of the best approximate decomposition (in a prescribed sense) if no exact decomposition is possible. It is proved that the best approximate decomposition exists and is unique up to some equivalence for every underdetermined source (for a decomposable source, it is its decomposition). A polynomial algorithm is described for constructing the best approximate decomposition. We study the problems connected with simplification and equivalent transformations of decompositions and propose some polynomial algorithms.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. P. Agibalov, Finite Automata on Semilattices (Tomsk. Gos. Univ., Tomsk, 1993) [in Russian].

    Google Scholar 

  2. R. Gallager, Information Theory and Reliable Communication (John Wiley & Sons, New York, 1968, Sovetskoe Radio, Moscow, 1974).

    MATH  Google Scholar 

  3. N. G. Parvatov, “Functional Completeness in Closed Classes of Quasimonotone and Monotone Three-Valued Functions on a Semilattice,” Diskretn. Anal. Issled. Oper. Ser. 1, 10(1), 61–78 (2003).

    MathSciNet  MATH  Google Scholar 

  4. N. G. Parvatov, “On Representation Forms of Monotone and Quasimonotone Functions on a Three-Element Semilattice,” in Proceedings of the IX International Workshop on Discrete Mathematics and Its Applications (Mekh.-Mat. Fakultet, Moskov. Gos. Univ., Moscow, 2007), pp. 127–130.

    Google Scholar 

  5. L. A. Sholomov, “Transformation of Fuzzy Data with Preservation of Information Properties,” Diskretn. Anal. Issled. Oper. Ser. 1, 12(3), 85–104 (2005).

    MathSciNet  MATH  Google Scholar 

  6. L. A. Sholomov, “Elements of Underdetermined Information Theory,” Prikl. Diskretn. Mat. Suppl. 2, 18–42 (2009).

  7. L. A. Sholomov, “Decomposition of Underdetermined Data,” in Problems of Theoretical Cybernetics. Proceedings of XVI International Conference (Nizhegorodsk. Gos. Univ., Nizhnii Novgorod, 2011), pp. 570–573.

    Google Scholar 

  8. S. V. Yablonskii, Elements of Mathematical Cybernetics (Vyssh. Shkola, Moscow, 2007) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. A. Sholomov.

Additional information

Original Russian Text © L.A. Sholomov, 2012, published in Diskretnyi Analiz i Issledovanie Operatsii, 2012, Vol. 19, No. 6, pp. 72–98.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sholomov, L.A. Decomposition of underdetermined data. J. Appl. Ind. Math. 7, 100–116 (2013). https://doi.org/10.1134/S1990478913010109

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478913010109

Keywords

Navigation