{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:59Z","timestamp":1747198079251,"version":"3.40.5"},"reference-count":42,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BSAB\/150401\/2019","UIDB\/00324\/2020"],"award-info":[{"award-number":["SFRH\/BSAB\/150401\/2019","UIDB\/00324\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We approach the study of complete bifix decodings of (uniformly) recurrent languages with\nthe help of free profinite monoids. We show that the complete bifix decoding of a uniformly recurrent language <jats:italic>F<\/jats:italic>\nby an <jats:italic>F<\/jats:italic>-charged rational complete bifix code is uniformly recurrent. An analogous result is obtained for recurrent languages.\nAs an application of the machinery developed within this approach, we show that the maximal pronilpotent quotient of the Sch\u00fctzenberger group of an irreducible symbolic dynamical system is an invariant of eventual conjugacy.<\/jats:p>","DOI":"10.1515\/forum-2022-0246","type":"journal-article","created":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T09:35:22Z","timestamp":1687944922000},"page":"1021-1045","source":"Crossref","is-referenced-by-count":0,"title":["A profinite approach to complete bifix decodings of recurrent languages"],"prefix":"10.1515","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5906-965X","authenticated-orcid":false,"given":"Alfredo","family":"Costa","sequence":"first","affiliation":[{"name":"University of Coimbra , CMUC , Department of Mathematics , Largo D. Dinis, 3001-143 Coimbra , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2023,6,29]]},"reference":[{"key":"2023070412445570263_j_forum-2022-0246_ref_001","doi-asserted-by":"crossref","unstructured":"J.  Almeida,\nFinite Semigroups and Universal Algebra,\nSer. Algebra 3,\nWorld Scientific, River Edge, 1994.","DOI":"10.1142\/2481"},{"key":"2023070412445570263_j_forum-2022-0246_ref_002","doi-asserted-by":"crossref","unstructured":"J.  Almeida,\nDynamics of finite semigroups,\nSemigroups, Algorithms, Automata and Languages,\nWorld Scientific, River Edge (2002), 269\u2013292.","DOI":"10.1142\/9789812776884_0009"},{"key":"2023070412445570263_j_forum-2022-0246_ref_003","doi-asserted-by":"crossref","unstructured":"J.  Almeida,\nProfinite semigroups and applications,\nStructural Theory of Automata, Semigroups, and Universal Algebra,\nNATO Sci. Ser. II Math. Phys. Chem. 207,\nSpringer, Dordrecht (2005), 1\u201345.","DOI":"10.1007\/1-4020-3817-8_1"},{"key":"2023070412445570263_j_forum-2022-0246_ref_004","doi-asserted-by":"crossref","unstructured":"J.  Almeida and A.  Costa,\nInfinite-vertex free profinite semigroupoids and symbolic dynamics,\nJ. Pure Appl. Algebra 213 (2009), no. 5, 605\u2013631.","DOI":"10.1016\/j.jpaa.2008.08.009"},{"key":"2023070412445570263_j_forum-2022-0246_ref_005","doi-asserted-by":"crossref","unstructured":"J.  Almeida and A.  Costa,\nPresentations of Sch\u00fctzenberger groups of minimal subshifts,\nIsrael J. Math. 196 (2013), no. 1, 1\u201331.","DOI":"10.1007\/s11856-012-0139-4"},{"key":"2023070412445570263_j_forum-2022-0246_ref_006","doi-asserted-by":"crossref","unstructured":"J.  Almeida and A.  Costa,\nA geometric interpretation of the Sch\u00fctzenberger group of a minimal subshift,\nArk. Mat. 54 (2016), no. 2, 243\u2013275.","DOI":"10.1007\/s11512-016-0233-7"},{"key":"2023070412445570263_j_forum-2022-0246_ref_007","doi-asserted-by":"crossref","unstructured":"J.  Almeida, A.  Costa, J. C.  Costa and M.  Zeitoun,\nThe linear nature of pseudowords,\nPubl. Mat. 63 (2019), no. 2, 361\u2013422.","DOI":"10.5565\/PUBLMAT6321901"},{"key":"2023070412445570263_j_forum-2022-0246_ref_008","doi-asserted-by":"crossref","unstructured":"J.  Almeida, A.  Costa, R.  Kyriakoglou and D.  Perrin,\nOn the group of a rational maximal bifix code,\nForum Math. 32 (2020), no. 3, 553\u2013576.","DOI":"10.1515\/forum-2018-0270"},{"key":"2023070412445570263_j_forum-2022-0246_ref_009","doi-asserted-by":"crossref","unstructured":"J.  Almeida, A.  Costa, R.  Kyriakoglou and D.  Perrin,\nProfinite Semigroups and Symbolic Dynamics,\nLecture Notes in Math. 2274,\nSpringer, Cham, 2020.","DOI":"10.1007\/978-3-030-55215-2"},{"key":"2023070412445570263_j_forum-2022-0246_ref_010","doi-asserted-by":"crossref","unstructured":"J.  Almeida and M. V.  Volkov,\nSubword complexity of profinite words and subgroups of free profinite semigroups,\nInternat. J. Algebra Comput. 16 (2006), no. 2, 221\u2013258.","DOI":"10.1142\/S0218196706002883"},{"key":"#cr-split#-2023070412445570263_j_forum-2022-0246_ref_011.1","unstructured":"Z. Alme\u012dda, Profinite groups associated with weakly primitive substitutions (in Russian), Fundam. Prikl. Mat. 11 (2005), no. 3, 13-48"},{"key":"#cr-split#-2023070412445570263_j_forum-2022-0246_ref_011.2","doi-asserted-by":"crossref","unstructured":"translation in J. Math. Sci 144 (2007), no. 2 3881-3903.","DOI":"10.1007\/s10958-007-0242-y"},{"key":"2023070412445570263_j_forum-2022-0246_ref_012","doi-asserted-by":"crossref","unstructured":"J.  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