{"id":"https://openalex.org/W2023484340","doi":"https://doi.org/10.1142/s0218196712500208","title":"DETERMINATIONS OF WEIGHTED FINITE AUTOMATA OVER COMMUTATIVE IDEMPOTENT MF-SEMIRINGS","display_name":"DETERMINATIONS OF WEIGHTED FINITE AUTOMATA OVER COMMUTATIVE IDEMPOTENT MF-SEMIRINGS","publication_year":2011,"publication_date":"2011-11-13","ids":{"openalex":"https://openalex.org/W2023484340","doi":"https://doi.org/10.1142/s0218196712500208","mag":"2023484340"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196712500208","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500208","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"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 Algebra and Computation","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/A5112323734","display_name":"Yong He","orcid":null},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"YONG HE","raw_affiliation_strings":["Key Laboratory of Knowledge Processing and Networked Manufacturing, School of Computer Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, P. R. China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Knowledge Processing and Networked Manufacturing, School of Computer Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, P. R. China","institution_ids":["https://openalex.org/I121296143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060080813","display_name":"Gongcai Xin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210133467","display_name":"Xi'an Aeronautical University","ror":"https://ror.org/03qn8zy63","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210133467"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"GONGCAI XIN","raw_affiliation_strings":["Department of Aerial Instrument and Electric Engineering, The First Aeronautical Institute of Air Force, Xinyang, Hubei 464000, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Aerial Instrument and Electric Engineering, The First Aeronautical Institute of Air Force, Xinyang, Hubei 464000, P. R. China","institution_ids":["https://openalex.org/I4210133467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060844551","display_name":"Zhi\u2010Xi Wang","orcid":"https://orcid.org/0000-0001-9908-204X"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"ZHIXI WANG","raw_affiliation_strings":["Key Laboratory of Knowledge Processing and Networked Manufacturing, School of Computer Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, P. R. China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Knowledge Processing and Networked Manufacturing, School of Computer Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, P. R. China","institution_ids":["https://openalex.org/I121296143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112323734"],"corresponding_institution_ids":["https://openalex.org/I121296143"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10056315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"03","first_page":"1250020","last_page":"1250020"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10911","display_name":"Chemical Synthesis and Analysis","score":0.984499990940094,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semiring","display_name":"Semiring","score":0.9714169502258301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8771227598190308},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.8266584873199463},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.6778035759925842},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5295907855033875},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.510251522064209},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48157739639282227},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4756219685077667},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.47182497382164},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4192482829093933},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40694183111190796},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08574900031089783}],"concepts":[{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.9714169502258301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8771227598190308},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.8266584873199463},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6778035759925842},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5295907855033875},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.510251522064209},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48157739639282227},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4756219685077667},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.47182497382164},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4192482829093933},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40694183111190796},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08574900031089783},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196712500208","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500208","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"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 Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W123022540","https://openalex.org/W151848917","https://openalex.org/W1552185717","https://openalex.org/W1966299098","https://openalex.org/W1993033486","https://openalex.org/W2002014927","https://openalex.org/W2037367360","https://openalex.org/W2061168833","https://openalex.org/W2067829889","https://openalex.org/W2118662970","https://openalex.org/W2125529971","https://openalex.org/W2143658255","https://openalex.org/W2327816196","https://openalex.org/W3013232094"],"related_works":["https://openalex.org/W2373496770","https://openalex.org/W1981365019","https://openalex.org/W2365154421","https://openalex.org/W4385681521","https://openalex.org/W4367694502","https://openalex.org/W2356435810","https://openalex.org/W4226452061","https://openalex.org/W4312619976","https://openalex.org/W1522032747","https://openalex.org/W2862035520"],"abstract_inverted_index":{"The":[0],"semirings":[1],"admitting":[2],"maximal":[3,30],"factorizations":[4],"of":[5,32],"any":[6],"finite":[7,63],"dimension":[8,33],"are":[9,91],"called":[10],"MF-semirings.":[11],"We":[12],"first":[13],"show":[14],"that":[15,60],"a":[16,29,44,61,69,74],"commutative":[17,70],"semiring":[18,47],"K":[19,27,42],"is":[20,43],"an":[21],"MF-semiring":[22,72],"if":[23,26,38,41,76],"and":[24,37,39,84],"only":[25,40],"admits":[28],"factorization":[31],"n":[34],"\u2265":[35],"2,":[36],"multiplicatively":[45],"cancellative":[46],"satisfying":[48],"the":[49,81],"g.c.d.":[50],"condition.":[51],"And":[52],"then,":[53],"by":[54],"using":[55],"above":[56],"result,":[57],"we":[58],"prove":[59],"weighted":[62],"automaton":[64],"[Formula:":[65,77],"see":[66,78],"text]":[67,79],"over":[68],"idempotent":[71],"has":[73,80],"determination":[75],"victory":[82],"property":[83],"twins":[85],"property.":[86],"Also,":[87],"some":[88],"special":[89],"cases":[90],"considered.":[92]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}