Skip to main content

On the direct sum conjecture in the straight line model

  • Conference paper
  • First Online:
Algorithms—ESA '93 (ESA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 726))

Included in the following conference series:

Abstract

We prove that if a quadratic system satisfies the direct sum conjecture strongly in the quadratic algorithm model, then it satisfies the direct sum conjecture strongly in the straight line algorithm model. Therefore, if the strong direct sum conjecture is true for the quadratic algorithm model then it is also true for the straight line algorithm model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Averbuch, Z. Galil, S. Winograd, Classification of all the minimal bilinear algorithms for computing the coefficient of the product of two polynomials modulo a polynomial in the algebra G[u]/<un>.

    Google Scholar 

  2. A. Averbuch, Z. Galil, S. Winograd, Classification of all the minimal bilinear algorithms for computing the coefficient of the product of two polynomials modulo a polynomial in the algebra G[u]/<Q(u)l> l>1, Theoretical Computer Science 58 (1988), 17–56.

    Google Scholar 

  3. N. H. Bshouty, On the extended direct sum conjecture, Proceedings 21st Annual ACM Symposium on Theory of Computing, (May 1989).

    Google Scholar 

  4. E. Feig, On systems of bilinear forms whose minimal division-free algorithms are all bilinear, Journal of Algorithms, 2, (1981), 261–281.

    Google Scholar 

  5. E. Feig, Certain systems of bilinear forms whose minimal algorithms are all quadratic, Journal of Algorithms, 4, (1983), 137–149.

    Google Scholar 

  6. A. Fellmann, Optimal algorithms for finite dimensional simply generated algebras, Lecture Notes in Computer Science, (1986).

    Google Scholar 

  7. E. Feig, S. Winograd, On the direct sum conjecture, Linear Algebra and Its Application, 63 (1984), 193–219.

    Google Scholar 

  8. C.M. Feduccia, Y. Zalcstein, Algebras having linear multiplicative complexity, J. ACM, 24 (1977), 311–331.

    Google Scholar 

  9. H. F. Groote, Characterization of division algebras of minimal rank and the structure of their algorithm varieties, SIAM J. Comput. 12 (1983), 101–117.

    Google Scholar 

  10. H. G. Groote, Lectures on the complexity of bilinear problems. LN Comput. Sci. 245, Springer, Berline 1987.

    Google Scholar 

  11. J. Ja' Ja', J. Takche, On the validity of the direct sum conjecture, SIAM. J.Comput, 15, 4, (1986), 1004–1020.

    Google Scholar 

  12. V. Strassen, Vermeidung von Divisionen, J. Reine Angew. Math. 264 (1973), 184–202.

    Google Scholar 

  13. S. Winograd, Some Bilinear Forms Whose Multiplicative Complexity Depends on the Field Constants, Math. System Theory, 10 (1976/77), 169–180.

    Google Scholar 

  14. S. Winograd, On multiplication in algebraic extension field, Theoret. Comput. Sci., 8 (1979), 359–377.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Thomas Lengauer

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bshouty, N.H. (1993). On the direct sum conjecture in the straight line model. In: Lengauer, T. (eds) Algorithms—ESA '93. ESA 1993. Lecture Notes in Computer Science, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57273-2_46

Download citation

  • DOI: https://doi.org/10.1007/3-540-57273-2_46

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57273-2

  • Online ISBN: 978-3-540-48032-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics