Generic complexity of the Conjugacy Problem in HNN-extensions and algorithmic stratification of Miller's groups
Group Theory
2009-03-24 v1
Abstract
We discuss time complexity of The Conjugacy Problem in HNN-extensions of groups, in particular, in Miller's groups. We show that for "almost all", in some explicit sense, elements, the Conjugacy Problem is decidable in cubic time. It is worth noting that the Conjugacy Problem in a Miller group may have be undecidable. Our results show that "hard" instances of the problem comprise a negligibly small part of the group.
Keywords
Cite
@article{arxiv.0903.3754,
title = {Generic complexity of the Conjugacy Problem in HNN-extensions and algorithmic stratification of Miller's groups},
author = {Alexandre V. Borovik and Alexei G. Myasnikov and Vladimir N. Remeslennikov},
journal= {arXiv preprint arXiv:0903.3754},
year = {2009}
}