Quadratic equations over free groups are NP-complete
O. Kharlampovich, I.G. Lysenok, A.G Myasnikov, N.W.M. Touikan
TL;DR
This paper proves that determining the solvability of quadratic equations over free groups is an NP-complete problem, highlighting its computational complexity.
Contribution
It establishes the NP-completeness of quadratic equations over free groups, a previously unresolved computational complexity classification.
Findings
Deciding solutions is NP-complete
Quadratic equations over free groups are computationally hard
Complexity classification of this problem
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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