Word problems recognisable by deterministic blind monoid automata

Kambites, Mark (2006) Word problems recognisable by deterministic blind monoid automata. Theoretical Computer Science, 362 (1-3). pp. 232-237. ISSN 0304-3975

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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.

Item Type: Article
Uncontrolled Keywords: Group; Monoid; Automaton; Word problem; Finite index subgroup
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra
Depositing User: Ms Lucy van Russelt
Date Deposited: 27 Mar 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/726

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