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.
| Original language | English |
|---|---|
| Article number | 1 |
| Pages (from-to) | 66-78 |
| Number of pages | 13 |
| Journal | Experimental mathematics |
| Volume | 29 |
| Issue number | 1 |
| Early online date | 20 Feb 2018 |
| DOIs | |
| Publication status | Published - 2020 |
Keywords
- math.GR
- cs.LG
- 20F10, 68T05
- group theory
- polycyclic group
- conjugacy
- Machine learning
- non-commutative cryptography