{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T12:10:03Z","timestamp":1750162203590,"version":"3.41.0"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T00:00:00Z","timestamp":1744761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T00:00:00Z","timestamp":1744761600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["# 11861071","# 11861071"],"award-info":[{"award-number":["# 11861071","# 11861071"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Graduate Student Research and Innovation Foundation of Yunnan University","award":["# KC- 22221163","# KC- 22221163","# KC- 22221163"],"award-info":[{"award-number":["# KC- 22221163","# KC- 22221163","# KC- 22221163"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Acta Informatica"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s00236-025-00487-x","type":"journal-article","created":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T18:07:20Z","timestamp":1744826840000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Three-word codes $$\\{a,\\ aba,\\ u\\}$$ and $$\\{a,\\ ab,\\ v\\}$$ having finite completions"],"prefix":"10.1007","volume":"62","author":[{"given":"Chunhua","family":"Cao","sequence":"first","affiliation":[]},{"given":"Lei","family":"Liao","sequence":"additional","affiliation":[]},{"given":"Zhongmei","family":"Yan","sequence":"additional","affiliation":[]},{"given":"Di","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Yuguang","family":"Yuan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,16]]},"reference":[{"key":"487_CR1","volume-title":"Codes and Automata","author":"J Berstel","year":"2010","unstructured":"Berstel, J., Perrin, D., Reutenauer, C.: Codes and Automata. Cambridge University Press, England (2010)"},{"key":"487_CR2","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0304-3975(95)00139-5","volume":"163","author":"D Derencourt","year":"1996","unstructured":"Derencourt, D.: A three-word code which is not prefix-suffix composed. Theoret. Comput. Sci. 163, 145\u2013160 (1996)","journal-title":"Theoret. Comput. Sci."},{"key":"487_CR3","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1051\/ita\/1986200100891","volume":"20","author":"A Ehrenfeucht","year":"1986","unstructured":"Ehrenfeucht, A., Rozenberg, G.: Each regular code is included in a maximal regular code. RAIRO-Theor. Inf. Appl. 20, 89\u201396 (1986)","journal-title":"RAIRO-Theor. Inf. Appl."},{"key":"487_CR4","first-page":"311","volume":"21","author":"S Konstantinidis","year":"2016","unstructured":"Konstantinidis, S., Mastnak, M.: Embedding rationally independent languages into maximal ones. J. Autom. Lang. Comb. 21, 311\u2013338 (2016)","journal-title":"J. Autom. Lang. Comb."},{"key":"487_CR5","first-page":"483","volume":"30","author":"NH Lam","year":"1994","unstructured":"Lam, N.H.: On codes having no finite completion. RAIRO-Theor. Inf. Appl. 30, 483\u2013493 (1994)","journal-title":"RAIRO-Theor. Inf. Appl."},{"key":"487_CR6","first-page":"57","volume":"31","author":"NH Lam","year":"2003","unstructured":"Lam, N.H.: Completing solid codes to maximal comma-free codes. Vietnam J. Math. 31, 57\u201369 (2003)","journal-title":"Vietnam J. Math."},{"key":"487_CR7","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1016\/S0304-3975(02)00595-9","volume":"301","author":"NH Lam","year":"2003","unstructured":"Lam, N.H.: Completing comma-free codes. Theoret. Comput. Sci. 301, 399\u2013415 (2003)","journal-title":"Theoret. Comput. Sci."},{"key":"487_CR8","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/0304-3975(94)00300-8","volume":"145","author":"Z Liang","year":"1995","unstructured":"Liang, Z., Zhonghui, S.: Completion of recognizable bifix codes. Theoret. Comput. Sci. 145, 345\u2013355 (1995)","journal-title":"Theoret. Comput. Sci."},{"key":"487_CR9","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/978-3-540-31834-7_23","volume":"3354","author":"J N\u00e9raud","year":"2005","unstructured":"N\u00e9raud, J.: Completing a code in a regular submonoid of the free monoid Machines, Computations, and Universality MCU 2004. Lecture Notes in Computer Science 3354, 281\u2013291 (2005)","journal-title":"Lecture Notes in Computer Science"},{"key":"487_CR10","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/j.tcs.2006.01.027","volume":"356","author":"J N\u00e9raud","year":"2006","unstructured":"N\u00e9raud, J.: Completing prefix codes in submonoids. Theoret. Comput. Sci. 356, 245\u2013254 (2006)","journal-title":"Theoret. Comput. Sci."},{"key":"487_CR11","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.tcs.2007.10.033","volume":"391","author":"J N\u00e9raud","year":"2008","unstructured":"N\u00e9raud, J.: Completing circular codes in regular submonoids. Theoret. Comput. Sci. 391, 90\u201398 (2008)","journal-title":"Theoret. Comput. Sci."},{"key":"487_CR12","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/S0304-3975(99)00160-7","volume":"255","author":"J N\u00e9raud","year":"2001","unstructured":"N\u00e9raud, J., Selmi, C.: On codes with a finite deciphering delay: constructing uncompletable words. Theoret. Comput. Sci. 255, 151\u2013162 (2001)","journal-title":"Theoret. Comput. Sci."},{"key":"487_CR13","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1142\/S0218196703001584","volume":"13","author":"J N\u00e9raud","year":"2003","unstructured":"N\u00e9raud, J., Selmi, C.: Free monoid theory: maximality and completeness in arbitrary submonoids. Int. J. Algebra Comput. 13, 507\u2013516 (2003)","journal-title":"Int. J. Algebra Comput."},{"key":"487_CR14","first-page":"103","volume":"9","author":"J N\u00e9raud","year":"2004","unstructured":"N\u00e9raud, J., Selmi, C.: A characterization of complete finite prefix codes in arbitrary submonoids of $$a^*$$. J. Autom. Lang. Comb. 9, 103\u2013110 (2004)","journal-title":"J. Autom. Lang. Comb."},{"key":"487_CR15","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.tcs.2018.08.022","volume":"806","author":"J N\u00e9raud","year":"2020","unstructured":"N\u00e9raud, J., Selmi, C.: Embedding a $$\\theta $$-invariant code into a complete one. Theoret. Comput. Sci. 806, 28\u201341 (2020)","journal-title":"Theoret. Comput. Sci."},{"key":"487_CR16","doi-asserted-by":"crossref","unstructured":"Pin, J.-A.: Handbook of Automata Theory Volume I. European Mathematical Society Press, Germany (2021)","DOI":"10.4171\/automata-2"},{"key":"487_CR17","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/0012-365X(77)90164-9","volume":"17","author":"A Restivo","year":"1977","unstructured":"Restivo, A.: On codes having no finite completions. Discret. Math. 17, 309\u2013316 (1977)","journal-title":"Discret. Math."},{"key":"487_CR18","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1051\/ita\/1989230201351","volume":"23","author":"A Restivo","year":"1989","unstructured":"Restivo, A., Salemi, S., Sportelli, T.: Completing codes. RAIRO-Theor. Inf. Appl. 23, 135\u2013147 (1989)","journal-title":"RAIRO-Theor. Inf. Appl."},{"key":"487_CR19","volume-title":"Free Monoids and Languages","author":"HJ Shyr","year":"2001","unstructured":"Shyr, H.J.: Free Monoids and Languages. Hon Min Book Company, Taiwan, Taichung (2001)"},{"key":"487_CR20","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/S0304-3975(03)00243-3","volume":"306","author":"L Zhang","year":"2003","unstructured":"Zhang, L., Shum, K.P., Peng, S.L.: Compltion of codes with finite bi-decoding delay. Theoret. Comput. Sci. 306, 123\u2013137 (2003)","journal-title":"Theoret. Comput. Sci."}],"container-title":["Acta Informatica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00236-025-00487-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00236-025-00487-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00236-025-00487-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T11:42:37Z","timestamp":1750160557000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00236-025-00487-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,16]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["487"],"URL":"https:\/\/doi.org\/10.1007\/s00236-025-00487-x","relation":{},"ISSN":["0001-5903","1432-0525"],"issn-type":[{"type":"print","value":"0001-5903"},{"type":"electronic","value":"1432-0525"}],"subject":[],"published":{"date-parts":[[2025,4,16]]},"assertion":[{"value":"27 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"20"}}