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
    • McGill University
  • I. G. Lysënok
    • Steklov Institute
  • A. G. Myasnikov
    • McGill University
    • McGill University

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


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


Equations over free groupsNP-completeness
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© Springer Science+Business Media, LLC 2008