Skip to main content
SpringerLink
Log in

Mathematics

Proof at a roll of the dice

  • News & Views
  • Published:

From Nature

View current issue Submit your manuscript

The PCP theorem encapsulates the idea that randomization allows the immediate verification of any mathematical proof. A simple route to this striking result was proposed earlier this year.

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

Figure 1: Probabilistically checkable colouring.

References

  1. Arora, S. & Safra, S. J. Assoc. Comput. Machin. 45, 70–122 (1998).

    Article  Google Scholar 

  2. Arora, S., Lund, C., Motwani, R., Sudan, M. & Szegedy, M. J. Assoc. Comput. Machin. 45, 501–555 (1998).

    Article  Google Scholar 

  3. Dinur, I. Proc. 38th Annu. ACM Symp. Theor. Comput. 241–250 (2006).

  4. Håstad, J. J. Assoc. Comput. Machin. 48, 798–859 (2001).

    Article  Google Scholar 

  5. Appel, K., Haken, W. & Koch, J. J. Math. 21, 439–567 (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Princeton University, 35 Olden Street, Princeton, 08540-5233, New Jersey, USA

    Bernard Chazelle

Authors
  1. Bernard Chazelle
    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

Chazelle, B. Proof at a roll of the dice. Nature 444, 1018–1019 (2006). https://doi.org/10.1038/4441018a

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/4441018a

  • Springer Nature Limited

Search

Navigation