{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T13:52:30Z","timestamp":1649080350420},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100006753","name":"Centro de Matem\u00e1tica Universidade do Porto","doi-asserted-by":"crossref","award":["UID\/MAT\/00144\/2013"],"award-info":[{"award-number":["UID\/MAT\/00144\/2013"]}],"id":[{"id":"10.13039\/501100006753","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"crossref","award":["336983"],"award-info":[{"award-number":["336983"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003086","name":"Eusko Jaurlaritza","doi-asserted-by":"crossref","award":["IT974-16"],"award-info":[{"award-number":["IT974-16"]}],"id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"crossref","award":["MTM2014-53810-C2-2-P"],"award-info":[{"award-number":["MTM2014-53810-C2-2-P"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Russian Foundation for Basic Research","award":["15-01-05823"],"award-info":[{"award-number":["15-01-05823"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that it is decidable whether or not a finitely generated submonoid of a virtually free group is graded, introduce a new geometric characterization of graded submonoids in virtually free groups as quasi-geodesic submonoids, and show that their word problem is rational (as a relation).\nWe also solve the isomorphism problem for this class of monoids, generalizing earlier results for submonoids of free monoids.\nWe also prove that the classes of graded monoids, regular monoids and Kleene monoids coincide for submonoids of free groups.<\/jats:p>","DOI":"10.1515\/gcc-2018-0008","type":"journal-article","created":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T15:52:12Z","timestamp":1611330732000},"page":"63-82","source":"Crossref","is-referenced-by-count":0,"title":["On finitely generated submonoids of virtually free groups"],"prefix":"10.1515","volume":"10","author":[{"given":"Pedro V.","family":"Silva","sequence":"first","affiliation":[{"name":"Centre of Mathematics, University of Porto, R. Campo Alegre 687, 4169-007Porto, Portugal"}]},{"given":"Alexander","family":"Zakharov","sequence":"additional","affiliation":[{"name":"Centre of Mathematics, University of Porto, R. Campo Alegre 687, 4169-007Porto, Portugal"}]}],"member":"374","container-title":["Groups Complexity Cryptology"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/gcc\/10\/2\/article-p63.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/gcc\/10\/2\/article-p63.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,27]],"date-time":"2021-02-27T03:08:51Z","timestamp":1614395331000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gcc-2018-0008\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,1]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.1515\/gcc-2018-0008","relation":{},"ISSN":["1867-1144","1869-6104"],"issn-type":[{"value":"1867-1144","type":"print"},{"value":"1869-6104","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,1]]}}}