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

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Abstract

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

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Authors and Affiliations

  1. McGill University, Montreal, QC, Canada

    O. Kharlampovich, A. G. Myasnikov & N. W. M. Touikan

  2. Steklov Institute, Moscow, Russia

    I. G. Lysënok

Authors
  1. O. Kharlampovich
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  2. I. G. Lysënok
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  3. A. G. Myasnikov
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  4. N. W. M. Touikan
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Correspondence to N. W. M. Touikan.

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Kharlampovich, O., Lysënok, I.G., Myasnikov, A.G. et al. The Solvability Problem for Quadratic Equations over Free Groups is NP-Complete. Theory Comput Syst 47, 250–258 (2010). https://doi.org/10.1007/s00224-008-9153-7

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  • DOI: https://doi.org/10.1007/s00224-008-9153-7

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