{"id":"https://openalex.org/W4408494155","doi":"https://doi.org/10.1142/s0129054125500091","title":"Three-Word Codes {a,aba,u} Having a Finite Completion","display_name":"Three-Word Codes {a,aba,u} Having a Finite Completion","publication_year":2025,"publication_date":"2025-03-13","ids":{"openalex":"https://openalex.org/W4408494155","doi":"https://doi.org/10.1142/s0129054125500091"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054125500091","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054125500091","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102484794","display_name":"Chunhua Cao","orcid":null},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chunhua Cao","raw_affiliation_strings":["School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China"],"raw_orcid":"https://orcid.org/0009-0001-0371-3925","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111492694","display_name":"Z. Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongmei Yan","raw_affiliation_strings":["School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China"],"raw_orcid":"https://orcid.org/0009-0006-0254-576X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113717399","display_name":"Yali Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I10660446","display_name":"Kunming University of Science and Technology","ror":"https://ror.org/00xyeez13","country_code":"CN","type":"education","lineage":["https://openalex.org/I10660446"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yali Yang","raw_affiliation_strings":["School of Science and Technology, Kunming University of Science, and Technology Oxbridge College, No. 1268 Haiyuan North Road, Kunming 650106, Yunnan Province, China"],"raw_orcid":"https://orcid.org/0009-0003-4131-572X","affiliations":[{"raw_affiliation_string":"School of Science and Technology, Kunming University of Science, and Technology Oxbridge College, No. 1268 Haiyuan North Road, Kunming 650106, Yunnan Province, China","institution_ids":["https://openalex.org/I10660446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116645289","display_name":"Hao Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Xie","raw_affiliation_strings":["School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China"],"raw_orcid":"https://orcid.org/0009-0008-0723-587X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038892735","display_name":"Yingheng Li","orcid":"https://orcid.org/0009-0002-5552-6176"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingheng Li","raw_affiliation_strings":["School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China"],"raw_orcid":"https://orcid.org/0009-0002-5552-6176","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Yunnan University, East Outer Ring Road South, University Town, Chenggong District, Kunming 650504, Yunnan Province, China","institution_ids":["https://openalex.org/I189210763"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5102484794"],"corresponding_institution_ids":["https://openalex.org/I189210763"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02095137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"02","first_page":"291","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.6465297341346741},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5288287997245789},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4524851441383362},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4036327600479126},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3876498341560364},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.341036856174469}],"concepts":[{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.6465297341346741},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5288287997245789},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4524851441383362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4036327600479126},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3876498341560364},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.341036856174469},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054125500091","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054125500091","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2539203927","display_name":null,"funder_award_id":"#11861071","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5740235494","display_name":null,"funder_award_id":"#11871419","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W82956666","https://openalex.org/W1536222145","https://openalex.org/W1585751054","https://openalex.org/W1968850105","https://openalex.org/W1972853392","https://openalex.org/W2039849141","https://openalex.org/W2040416787","https://openalex.org/W2062991407","https://openalex.org/W2068469059","https://openalex.org/W2076024367","https://openalex.org/W2091274708","https://openalex.org/W2165183601","https://openalex.org/W2783291246","https://openalex.org/W3157844820","https://openalex.org/W4232006565","https://openalex.org/W4386784795"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"One-word":[0],"codes":[1,4,17,56],"and":[2,68],"two-word":[3],"are":[5,72],"prefix-suffix-composed":[6],"codes,":[7],"then":[8],"they":[9],"have":[10,19,31,64],"a":[11,32,52,65],"finite":[12,21,33,66],"completion.":[13],"There":[14],"exist":[15],"n-word":[16],"that":[18,63],"no":[20],"completion":[22,67],"when":[23],"[Formula:":[24,60],"see":[25,61],"text].":[26],"Does":[27],"every":[28],"three-word":[29,55,74],"code":[30],"completion?":[34],"Up":[35],"to":[36],"now,":[37],"this":[38,48],"famous":[39],"question":[40],"in":[41],"Theory":[42],"of":[43,54,70],"Codes":[44],"remains":[45],"open.":[46],"In":[47],"paper,":[49],"we":[50],"construct":[51],"series":[53],"with":[57],"the":[58],"form":[59],"text]":[62],"part":[69],"them":[71],"prefix-suffix-indecomposable":[73],"codes.":[75]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}