The word problem for free groups cannot be solved in linear time*
Group Theory
2022-02-14 v1 Combinatorics
Abstract
*by a standard (one-tape) Turing machine. It is well-known that the word problem for hyperbolic groups, whence in particular for free groups, can be solved in linear time. However, these algorithms run on machines more complicated than a standard Turing machine. By contrast, in this note we show that a standard Turing machine cannot solve the word problem for the free group on two generators in less than quadratic time.
Cite
@article{arxiv.2202.05787,
title = {The word problem for free groups cannot be solved in linear time*},
author = {Alessandro Sisto},
journal= {arXiv preprint arXiv:2202.05787},
year = {2022}
}
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2 pages