{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T22:56:18Z","timestamp":1648680978539},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2017,3]]},"abstract":"<jats:p> For a given finitely generated group [Formula: see text], the type of languages that are accepted by [Formula: see text]-automata is determined by the word problem of [Formula: see text] for most of the classical types of languages. We observe that the only exceptions are the families of context-sensitive and recursive languages. Thus, in general, to ensure that the language accepted by a [Formula: see text]-automaton is in the same classical family of languages as the word problem of [Formula: see text], some restriction must be imposed on the [Formula: see text]-automaton. We show that restricting to [Formula: see text]-automata without [Formula: see text]-transitions is sufficient for this purpose. We then define the pullback of two [Formula: see text]-automata and use this construction to study the closure properties of the family of languages accepted by [Formula: see text]-automata without [Formula: see text]-transitions. As a further consequence, when [Formula: see text] is the product of two groups, we give a characterization of the family of languages accepted by [Formula: see text]-automata in terms of the families of languages accepted by [Formula: see text]- and [Formula: see text]-automata. We also give a construction of a grammar for the language accepted by an arbitrary [Formula: see text]-automaton and show how to get a context-sensitive grammar when [Formula: see text] is finitely generated with a context-sensitive word problem and the [Formula: see text]-automaton is without [Formula: see text]-transitions. <\/jats:p>","DOI":"10.1142\/s0218196717500102","type":"journal-article","created":{"date-parts":[[2017,3,7]],"date-time":"2017-03-07T04:03:02Z","timestamp":1488859382000},"page":"237-249","source":"Crossref","is-referenced-by-count":0,"title":["Context-sensitive languages and G-automata"],"prefix":"10.1142","volume":"27","author":[{"given":"Rachel","family":"Bishop-Ross","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, KY 40475, USA"}]},{"given":"Jon M.","family":"Corson","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA"}]},{"given":"James Lance","family":"Ross","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Eastern Kentucky University, Richmond, KY 40475, USA"}]}],"member":"219","published-online":{"date-parts":[[2017,4,9]]},"reference":[{"key":"S0218196717500102BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-663-09367-1"},{"key":"S0218196717500102BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84800-940-0"},{"key":"S0218196717500102BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/s0129054115500045"},{"key":"S0218196717500102BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196705002360"},{"key":"S0218196717500102BIB006","first-page":"27","volume-title":"Geometric and Computational Perspectives on Infinite Groups","author":"Gilman R. H.","year":"1996"},{"key":"S0218196717500102BIB007","volume-title":"Formal Languages and Their Relation to Automata","author":"Hopcroft J. E.","year":"1969"},{"key":"S0218196717500102BIB008","doi-asserted-by":"publisher","DOI":"10.1080\/00927870802243580"},{"key":"S0218196717500102BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00200-6"},{"key":"S0218196717500102BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196794000129"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196717500102","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:24:56Z","timestamp":1565141096000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196717500102"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3]]},"references-count":9,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2017,4,9]]},"published-print":{"date-parts":[[2017,3]]}},"alternative-id":["10.1142\/S0218196717500102"],"URL":"https:\/\/doi.org\/10.1142\/s0218196717500102","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3]]}}}