On groups whose word problem is solved by a counter automaton

Authors:
Gillian Z. Elston;Gretchen Ostheimer
Affiliations:
Department of Mathematics, Hofstra University, Hempstead, NY;Department of Computer Science, Hofstra University, Hempstead, NY
Venue:
Theoretical Computer Science
Year:
2004

Citing 1
Cited 3

Automata, Languages, and Machines

Automata, Languages, and Machines

A context-free and a 1-counter geodesic language for a Baumslag-Solitar group

Theoretical Computer Science
Word problems recognisable by deterministic blind monoid automata

Theoretical Computer Science
Semigroup automata with rational initial and terminal sets

Theoretical Computer Science

Quantified Score

Hi-index	5.23

Visualization

Abstract

We prove that a group G has a word problem that is accepted by a deterministic counter automaton with a weak inverse property if and only if G is virtually abelian. We extend this result to larger classes of groups by considering a generalization of finite state automata, counter automata and pushdown automata. Natural corollaries of our general result include a restricted version of Herbst's classification of groups for which the word problem is a one counter language and a new classification of automata that accept context-free word problems.