{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T11:08:31Z","timestamp":1776942511728,"version":"3.51.4"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,12]]},"abstract":"<jats:p> 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\u2013Schupp theorem. More generally, if G is a virtually abelian group then every group with word problem recognized by a G-automaton is virtually abelian with growth class bounded above by the growth class of G. We consider also other types of counter automata. <\/jats:p>","DOI":"10.1142\/s0218196708004901","type":"journal-article","created":{"date-parts":[[2008,12,29]],"date-time":"2008-12-29T04:49:04Z","timestamp":1230526144000},"page":"1345-1364","source":"Crossref","is-referenced-by-count":17,"title":["ON GROUPS AND COUNTER AUTOMATA"],"prefix":"10.1142","volume":"18","author":[{"given":"MURRAY","family":"ELDER","sequence":"first","affiliation":[{"name":"Mathematics, University of Queensland, Brisbane QLD 4072, Australia"}]},{"given":"MARK","family":"KAMBITES","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Manchester, Manchester M13 9PL, England, UK"}]},{"given":"GRETCHEN","family":"OSTHEIMER","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Hofstra University, Hempstead, New York 11549, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700019108"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)72023-8"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196705002360"},{"key":"rf6","volume-title":"The Structure of Linear Groups","author":"Dixon J. 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