Whitehead method and Genetic Algorithms
群论
2007-05-23 v1 神经与进化计算
符号计算
摘要
In this paper we discuss a genetic version (GWA) of the Whitehead's algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisingly fast and outperforms the standard Whitehead's algorithm in free groups of rank >= 5. Experimenting with GWA we collected an interesting numerical data that clarifies the time-complexity of the Whitehead's Problem in general. These experiments led us to several mathematical conjectures. If confirmed they will shed light on hidden mechanisms of Whitehead Method and geometry of automorphic orbits in free groups.
引用
@article{arxiv.math/0304283,
title = {Whitehead method and Genetic Algorithms},
author = {Alexei D. Miasnikov and Alexei G. Myasnikov},
journal= {arXiv preprint arXiv:math/0304283},
year = {2007}
}
备注
29 pages, 7 figures