English

Groups that do and do not have context-sensitive word problem

Group Theory 2008-01-30 v1

Abstract

We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and Shapiro). We generalise their results to find many examples of groups not admitting non-deterministic Cannon's algorithms. This adds to the examples of Kambites and Otto of groups separating context-sensitive and growing context-sensitive word problems, and provides a new language-theoretic separation result.

Keywords

Cite

@article{arxiv.0801.4533,
  title  = {Groups that do and do not have context-sensitive word problem},
  author = {Derek F. Holt and Sarah Rees and Michael Shapiro},
  journal= {arXiv preprint arXiv:0801.4533},
  year   = {2008}
}
R2 v1 2026-06-21T10:07:36.693Z