Skip to main content

Tensor rank is NP-complete

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 372))

Included in the following conference series:

Abstract

We prove that computing the rank of a three-dimensional tensor over any finite field is NP-complete. Over the rational numbers the problem is NP-hard.

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. Alder A. and Strassen V. “On the Algorithmic Complexity of Associative Algebras”, Theoretical Computer Science 15 (1981), pp 201–211.

    Article  Google Scholar 

  2. Bshouty N.H. “A Lower Bound for Matrix Multiplication”, Proceedings 29th Annual IEEE Symposium on Foundations of Computer Science, 1988, pp 64–67.

    Google Scholar 

  3. Cook S.A. “On the Complexity of Theorem Proving Procedures”, Proceedings 3rd Annual ACM Symposium on the Theory of Computing, pp 151–159.

    Google Scholar 

  4. Coppersmith D. and Winograd S., “Matrix Multiplication via Arithmetic Progressions”, Proceedings 19th Annual ACM Symposium on the Theory of Computing, pp 1–6.

    Google Scholar 

  5. Garey M. R. and Johnson D.S., “Computers and Intractability”, W.H. Freeman and Company, 1979.

    Google Scholar 

  6. Gonzalez T. and Ja'Ja' J. “On the Complexity of Computing Bilinear Forms with {0, 1} Constants”, Journal of Computer and Systems Sciences 20, (1980) pp 77–95.

    Article  Google Scholar 

  7. Strassen V. “The asymptotic spectrum of tensors”, manuscript, 1986.

    Google Scholar 

  8. Strassen V. “Rank and Optimal Computation of Generic Tensors”, Linear Algebra and its applications 52/53 (1983), pp 645–685.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Giorgio Ausiello Mariangiola Dezani-Ciancaglini Simonetta Ronchi Della Rocca

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Håstad, J. (1989). Tensor rank is NP-complete. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds) Automata, Languages and Programming. ICALP 1989. Lecture Notes in Computer Science, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035776

Download citation

  • DOI: https://doi.org/10.1007/BFb0035776

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51371-1

  • Online ISBN: 978-3-540-46201-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics