Logspace and compressed-word computations in nilpotent groups
Group Theory
2021-12-21 v3 Computational Complexity
Abstract
For finitely generated nilpotent groups, we employ Mal'cev coordinates to solve several classical algorithmic problems efficiently. Computation of normal forms, the membership problem, the conjugacy problem, and computation of presentations for subgroups are solved using only logarithmic space and quasilinear time. Logarithmic space presentation-uniform versions of these algorithms are provided. Compressed-word versions of the same problems, in which each input word is provided as a straight-line program, are solved in polynomial time.
Cite
@article{arxiv.1503.03888,
title = {Logspace and compressed-word computations in nilpotent groups},
author = {Jeremy Macdonald and Alexei Myasnikov and Andrey Nikolaev and Svetla Vassileva},
journal= {arXiv preprint arXiv:1503.03888},
year = {2021}
}
Comments
Accepted in Transactions of the AMS