Theory of Computing Systems

, Volume 47, Issue 1, pp 250–258 | Cite as

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

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 groups NP-completeness 

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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

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