Theory of Computing Systems

, Volume 47, Issue 1, pp 250–258

The Solvability Problem for Quadratic Equations over Free Groups is NP-Complete

  • O. Kharlampovich
  • I. G. Lysënok
  • A. G. Myasnikov
  • N. W. M. Touikan
Article

DOI: 10.1007/s00224-008-9153-7

Cite this article as:
Kharlampovich, O., Lysënok, I.G., Myasnikov, A.G. et al. Theory Comput Syst (2010) 47: 250. doi:10.1007/s00224-008-9153-7

Abstract

We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete.

Keywords

Equations over free groupsNP-completeness

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • O. Kharlampovich
    • 1
  • I. G. Lysënok
    • 2
  • A. G. Myasnikov
    • 1
  • N. W. M. Touikan
    • 1
  1. 1.McGill UniversityMontrealCanada
  2. 2.Steklov InstituteMoscowRussia