{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:04:48Z","timestamp":1776726288909,"version":"3.51.2"},"reference-count":23,"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":[[2018,3]]},"abstract":"<jats:p> L systems generalize context-free grammars by incorporating parallel rewriting, and generate languages such as EDT0L and ET0L that are strictly contained in the class of indexed languages. In this paper, we show that many of the languages naturally appearing in group theory, and that were known to be indexed or context-sensitive, are in fact ET0L and in many cases EDT0L. For instance, the language of primitives and bases in the free group on two generators, the Bridson\u2013Gilman normal forms for the fundamental groups of 3-manifolds or orbifolds, and the co-word problem of Grigorchuk\u2019s group can be generated by L systems. To complement the result on primitives in rank 2 free groups, we show that the language of primitives, and primitive sets, in free groups of rank higher than two is context-sensitive. We also show the existence of EDT0L languages of intermediate growth. <\/jats:p>","DOI":"10.1142\/s0218196718500145","type":"journal-article","created":{"date-parts":[[2018,2,4]],"date-time":"2018-02-04T22:50:24Z","timestamp":1517784624000},"page":"309-329","source":"Crossref","is-referenced-by-count":13,"title":["Applications of L systems to group theory"],"prefix":"10.1142","volume":"28","author":[{"given":"Laura","family":"Ciobanu","sequence":"first","affiliation":[{"name":"School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland"}]},{"given":"Murray","family":"Elder","sequence":"additional","affiliation":[{"name":"University of Technology Sydney, Ultimo NSW 2007, Australia"}]},{"given":"Michal","family":"Ferov","sequence":"additional","affiliation":[{"name":"University of Technology Sydney, Ultimo NSW 2007, Australia"}]}],"member":"219","published-online":{"date-parts":[[2018,3,27]]},"reference":[{"key":"S0218196718500145BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(77)90308-4"},{"key":"S0218196718500145BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02566435"},{"key":"S0218196718500145BIB003","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.2001.1804"},{"key":"S0218196718500145BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)72023-8"},{"key":"S0218196718500145BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196716500363"},{"key":"S0218196718500145BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2012.01.033"},{"key":"S0218196718500145BIB007","doi-asserted-by":"publisher","DOI":"10.1080\/00207167408803079"},{"key":"S0218196718500145BIB008","series-title":"Chicago Lectures in Mathematics","volume-title":"Topics in Geometric Group Theory","author":"de la Harpe P.","year":"2000"},{"issue":"4","key":"S0218196718500145BIB011","first-page":"273","volume":"11","author":"Ehrenfeucht A.","year":"1977","journal-title":"ITA"},{"key":"S0218196718500145BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/BF00268142"},{"key":"S0218196718500145BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(76)90076-1"},{"key":"S0218196718500145BIB014","doi-asserted-by":"publisher","DOI":"10.1145\/322169.322178"},{"key":"S0218196718500145BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(96)00244-7"},{"key":"S0218196718500145BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(98)00161-3"},{"key":"S0218196718500145BIB017","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1195192738"},{"key":"S0218196718500145BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196706003359"},{"key":"S0218196718500145BIB020","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2001.9033"},{"key":"S0218196718500145BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/S021819671350001X"},{"key":"S0218196718500145BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/BF00288769"},{"key":"S0218196718500145BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-95486-3"},{"key":"S0218196718500145BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59126-6"},{"key":"S0218196718500145BIB027","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196710005790"},{"key":"S0218196718500145BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/BF02095993"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718500145","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:44:45Z","timestamp":1565171085000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718500145"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3]]},"references-count":23,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2018,3,27]]},"published-print":{"date-parts":[[2018,3]]}},"alternative-id":["10.1142\/S0218196718500145"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718500145","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3]]}}}