Word problems recognisable by deterministic blind monoid automata

Mark Kambites

Word problems recognisable by deterministic blind monoid automata

Group Theory 2007-05-23 v2

Authors: Mark Kambites

Abstract

We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class including groups, such an automaton accepts the word problem of a group H if and only if H has a finite index subgroup which embeds in the group of units of M. In the case that M is a group, this answers a question of Elston and Ostheimer.

Keywords

monoids sturmian words and combinatorics on words finite group theory

Cite

@article{arxiv.math/0506137,
  title  = {Word problems recognisable by deterministic blind monoid automata},
  author = {Mark Kambites},
  journal= {arXiv preprint arXiv:math/0506137},
  year   = {2007}
}