Word problems recognisable by deterministic blind monoid automata
Abstract
Description
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.
8 pages, fixed some typos and clarified ambiguity in the abstract, results unchanged
8 pages, fixed some typos and clarified ambiguity in the abstract, results unchanged