ON GROUPS AND COUNTER AUTOMATA

MURRAY ELDER, MARK KAMBITES, GRETCHEN OSTHEIMER
2008 International journal of algebra and computation  
We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this result, which answers a question of Gilman, is in a very precise sense an abelian analogue of the Muller-Schupp theorem. More generally, if G is a virtually abelian group then every group with word problem recognised by a G-automaton is virtually
more » ... maton is virtually abelian with growth class bounded above by the growth class of G. We consider also other types of counter automata.
doi:10.1142/s0218196708004901 fatcat:rvxdepp36zf75expa4j3es5mla