{"id":"https://openalex.org/W2087987102","doi":"https://doi.org/10.1142/s012905411100812x","title":"A KLEENE THEOREM FOR BISEMIGROUP AND BINOID LANGUAGES","display_name":"A KLEENE THEOREM FOR BISEMIGROUP AND BINOID LANGUAGES","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W2087987102","doi":"https://doi.org/10.1142/s012905411100812x","mag":"2087987102"},"language":"en","primary_location":{"id":"doi:10.1142/s012905411100812x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s012905411100812x","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/A5071606442","display_name":"Zsolt Gazdag","orcid":"https://orcid.org/0000-0002-5617-8743"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"ZSOLT GAZDAG","raw_affiliation_strings":["Faculty of Informatics, E\u00f6tv\u00f6s Lor\u00e1nd University, P.O.B. 120, 1518 Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Informatics, E\u00f6tv\u00f6s Lor\u00e1nd University, P.O.B. 120, 1518 Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103522954","display_name":"Zolt\u00e1n L. N\u00e9meth","orcid":null},"institutions":[{"id":"https://openalex.org/I227486990","display_name":"University of Szeged","ror":"https://ror.org/01pnej532","country_code":"HU","type":"education","lineage":["https://openalex.org/I227486990"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"ZOLT\u00c1N L. N\u00c9METH","raw_affiliation_strings":["Inst. of Informatics, University of Szeged, P.O.B. 652, 6701 Szeged, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inst. of Informatics, University of Szeged, P.O.B. 652, 6701 Szeged, Hungary","institution_ids":["https://openalex.org/I227486990"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14799577,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"02","first_page":"427","last_page":"446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9984999895095825,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9887999892234802,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/abstract-family-of-languages","display_name":"Abstract family of languages","score":0.604797899723053},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.5961968898773193},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5712525844573975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5476575493812561},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.5293959975242615},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.5122915506362915},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.4874477684497833},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4708758592605591},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4616388976573944},{"id":"https://openalex.org/keywords/kleene-algebra","display_name":"Kleene algebra","score":0.44768714904785156},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4400452971458435},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39024683833122253},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2554360032081604},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16572371125221252},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.1472678780555725},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.13613301515579224},{"id":"https://openalex.org/keywords/second-generation-programming-language","display_name":"Second-generation programming language","score":0.10211062431335449},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06103008985519409}],"concepts":[{"id":"https://openalex.org/C199163288","wikidata":"https://www.wikidata.org/wiki/Q3065587","display_name":"Abstract family of languages","level":5,"score":0.604797899723053},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.5961968898773193},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5712525844573975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5476575493812561},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.5293959975242615},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.5122915506362915},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4874477684497833},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4708758592605591},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4616388976573944},{"id":"https://openalex.org/C206470798","wikidata":"https://www.wikidata.org/wiki/Q2634506","display_name":"Kleene algebra","level":2,"score":0.44768714904785156},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4400452971458435},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39024683833122253},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2554360032081604},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16572371125221252},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.1472678780555725},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.13613301515579224},{"id":"https://openalex.org/C11164408","wikidata":"https://www.wikidata.org/wiki/Q18657800","display_name":"Second-generation programming language","level":4,"score":0.10211062431335449},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06103008985519409},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C50033165","wikidata":"https://www.wikidata.org/wiki/Q15712089","display_name":"Inductive programming","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C34165917","wikidata":"https://www.wikidata.org/wiki/Q188267","display_name":"Programming paradigm","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s012905411100812x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s012905411100812x","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W174797081","https://openalex.org/W1490858874","https://openalex.org/W1708589781","https://openalex.org/W1862901365","https://openalex.org/W1977595510","https://openalex.org/W1989683733","https://openalex.org/W2045594629","https://openalex.org/W2064845612","https://openalex.org/W2084235865","https://openalex.org/W2085767100","https://openalex.org/W2107260743","https://openalex.org/W2156824154","https://openalex.org/W2395711571","https://openalex.org/W2913236170"],"related_works":["https://openalex.org/W2017318974","https://openalex.org/W1998380256","https://openalex.org/W4254878942","https://openalex.org/W1979564497","https://openalex.org/W2105739157","https://openalex.org/W2591138383","https://openalex.org/W2240836793","https://openalex.org/W1540583425","https://openalex.org/W3049285863","https://openalex.org/W177851052"],"abstract_inverted_index":{"A":[0],"bisemigroup":[1,15,21,44,54],"is":[2,56],"a":[3,40,82,108],"set":[4],"with":[5],"two":[6,104],"associative":[7,105],"operations.":[8],"Subsets":[9],"of":[10,52,70,85,99],"free":[11,100],"bisemigroups":[12],"are":[13,30],"called":[14],"languages.":[16],"Recognizable,":[17],"regular":[18],"and":[19,27,65,73,77,81],"MSO-definable":[20],"languages":[22,55,64],"have":[23],"been":[24],"studied":[25],"earlier,":[26],"these":[28],"classes":[29],"known":[31],"to":[32,93,97],"be":[33],"equal.":[34],"In":[35],"this":[36],"paper":[37],"we":[38,47],"prove":[39],"Kleene":[41],"theorem":[42],"for":[43],"languages,":[45,95],"namely":[46],"show":[48],"that":[49],"the":[50,57,62,68,86,87,103],"class":[51,59],"recognizable":[53],"least":[58],"which":[60],"contains":[61],"finite":[63],"closed":[66],"under":[67],"operations":[69,106],"union,":[71],"horizontal":[72,76],"vertical":[74,78],"product,":[75],"iteration,":[79],"\u03be-substitution":[80],"restricted":[83],"version":[84],"\u03be-iteration.":[88],"We":[89],"extend":[90],"our":[91],"result":[92],"binoid":[94],"i.e.,":[96],"subsets":[98],"algebras,":[101],"where":[102],"share":[107],"common":[109],"identity":[110],"element.":[111]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}