Theory of Computing Systems

, Volume 47, Issue 1, pp 250-258

First online:

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

  • O. KharlampovichAffiliated withMcGill University
  • , I. G. LysënokAffiliated withSteklov Institute
  • , A. G. MyasnikovAffiliated withMcGill University
  • , N. W. M. TouikanAffiliated withMcGill University Email author 

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


Equations over free groups NP-completeness