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arXiv · 1705.10417

Solving the Conjugacy Decision Problem via Machine Learning

Jonathan Gryak·Robert M. Haralick·Delaram Kahrobaei
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Abstract

Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis on polycyclic and metabelian groups that are of interest to non-commutative cryptography. As a prototypical example, we utilize supervised learning methods to construct classifiers that can solve the conjugacy decision problem, i.e., determine whether or not a pair of elements from a specified group are conjugate. The accuracies of classifiers created using decision trees, random forests, and N-tuple neural network models are evaluated for several non-free groups. The very high accuracy of these classifiers suggests an underlying mathematical relationship with respect to conjugacy in the tested groups.

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Jonathan Gryak, Robert M. Haralick, Delaram Kahrobaei. 2018-02-21. Solving the Conjugacy Decision Problem via Machine Learning. https://arxiv.org/abs/1705.10417

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