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Word problems recognisable by deterministic blind monoid automata

Mark Kambites
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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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Mark Kambites. 2005-07-27. Word problems recognisable by deterministic blind monoid automata. https://arxiv.org/abs/math/0506137

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