Word problems recognisable by deterministic blind monoid automata

2005/06/08 by Mark Kambites, Kambites, Mark
Mathematics · #20F10 (Primary) #20M05 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F10 #msc:20M05

paper · pdf · doi:10.48550/arxiv.math/0506137

8 pages, fixed some typos and clarified ambiguity in the abstract, results unchanged

arxiv created 2005/07/27 · arxiv updated 2009/12/01

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.

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