The solvability problem for quadratic equations over free groups is NP-complete

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

doi:10.1007/s00224-008-9153-7

The solvability problem for quadratic equations over free groups is NP-complete

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

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	250-258
Number of pages	9
Journal	Mathematical Systems Theory
Volume	47
Issue number	1
DOIs	https://doi.org/10.1007/s00224-008-9153-7
State	Published - Jul 2010

Keywords

Equations over free groups
NP-completeness

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10.1007/s00224-008-9153-7

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title = "The solvability problem for quadratic equations over free groups is NP-complete",

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",

author = "O. Kharlampovich and Lys{\"e}nok, \{I. G.\} and Myasnikov, \{A. G.\} and Touikan, \{N. W.M.\}",

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language = "English",

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AU - Kharlampovich, O.

AU - Lysënok, I. G.

AU - Myasnikov, A. G.

AU - Touikan, N. W.M.

PY - 2010/7

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N2 - We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete.

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

KW - Equations over free groups

KW - NP-completeness

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JO - Mathematical Systems Theory

JF - Mathematical Systems Theory

IS - 1

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The solvability problem for quadratic equations over free groups is NP-complete

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Keywords

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