{"id":"https://openalex.org/W2248926456","doi":"https://doi.org/10.1051/ita/2015006","title":"On language equations with concatenation and various sets of Boolean operations","display_name":"On language equations with concatenation and various sets of Boolean operations","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W2248926456","doi":"https://doi.org/10.1051/ita/2015006","mag":"2248926456"},"language":"en","primary_location":{"id":"doi:10.1051/ita/2015006","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita/2015006","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.numdam.org/item/10.1051/ita/2015006.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005683089","display_name":"Alexander Okhotin","orcid":"https://orcid.org/0000-0002-1615-2725"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Alexander Okhotin","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland","institution_ids":["https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005683089"],"corresponding_institution_ids":["https://openalex.org/I155660961"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12660591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"3","first_page":"205","last_page":"232"},"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/T10181","display_name":"Natural Language Processing Techniques","score":0.996399998664856,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9958999752998352,"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/concatenation","display_name":"Concatenation (mathematics)","score":0.6654939651489258},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6108964681625366},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.5645139813423157},{"id":"https://openalex.org/keywords/context-free-language","display_name":"Context-free language","score":0.5136424899101257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5032810568809509},{"id":"https://openalex.org/keywords/abstract-family-of-languages","display_name":"Abstract family of languages","score":0.49615296721458435},{"id":"https://openalex.org/keywords/formal-language","display_name":"Formal language","score":0.47844696044921875},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47364723682403564},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4539281725883484},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43084949254989624},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.427043616771698},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.36810219287872314},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35566258430480957},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3288966417312622},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32039815187454224},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2659359574317932},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.2513132691383362},{"id":"https://openalex.org/keywords/rule-based-machine-translation","display_name":"Rule-based machine translation","score":0.24698874354362488},{"id":"https://openalex.org/keywords/fifth-generation-programming-language","display_name":"Fifth-generation programming language","score":0.17281204462051392},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13519126176834106},{"id":"https://openalex.org/keywords/second-generation-programming-language","display_name":"Second-generation programming language","score":0.0864584743976593},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.0788792073726654},{"id":"https://openalex.org/keywords/programming-paradigm","display_name":"Programming paradigm","score":0.06969764828681946}],"concepts":[{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.6654939651489258},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6108964681625366},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.5645139813423157},{"id":"https://openalex.org/C198838072","wikidata":"https://www.wikidata.org/wiki/Q729271","display_name":"Context-free language","level":3,"score":0.5136424899101257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5032810568809509},{"id":"https://openalex.org/C199163288","wikidata":"https://www.wikidata.org/wiki/Q3065587","display_name":"Abstract family of languages","level":5,"score":0.49615296721458435},{"id":"https://openalex.org/C146072743","wikidata":"https://www.wikidata.org/wiki/Q192161","display_name":"Formal language","level":2,"score":0.47844696044921875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47364723682403564},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4539281725883484},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43084949254989624},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.427043616771698},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.36810219287872314},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35566258430480957},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3288966417312622},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32039815187454224},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2659359574317932},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.2513132691383362},{"id":"https://openalex.org/C53893814","wikidata":"https://www.wikidata.org/wiki/Q7378909","display_name":"Rule-based machine translation","level":2,"score":0.24698874354362488},{"id":"https://openalex.org/C199305712","wikidata":"https://www.wikidata.org/wiki/Q3205914","display_name":"Fifth-generation programming language","level":3,"score":0.17281204462051392},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13519126176834106},{"id":"https://openalex.org/C11164408","wikidata":"https://www.wikidata.org/wiki/Q18657800","display_name":"Second-generation programming language","level":4,"score":0.0864584743976593},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0788792073726654},{"id":"https://openalex.org/C34165917","wikidata":"https://www.wikidata.org/wiki/Q188267","display_name":"Programming paradigm","level":2,"score":0.06969764828681946},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ita/2015006","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita/2015006","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:ITA_2015__49_3_205_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ita/2015006/","pdf_url":"https://www.numdam.org/item/10.1051/ita/2015006.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:numdam.org:ITA_2015__49_3_205_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ita/2015006/","pdf_url":"https://www.numdam.org/item/10.1051/ita/2015006.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5600000023841858,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3365925516","display_name":null,"funder_award_id":"257857","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G4769367927","display_name":null,"funder_award_id":"118540","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G5610805640","display_name":null,"funder_award_id":"134860","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"}],"funders":[{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2248926456.pdf","grobid_xml":"https://content.openalex.org/works/W2248926456.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W49473404","https://openalex.org/W113648983","https://openalex.org/W649821374","https://openalex.org/W1480450127","https://openalex.org/W1496259111","https://openalex.org/W1512779672","https://openalex.org/W1523067754","https://openalex.org/W1546744587","https://openalex.org/W1560143702","https://openalex.org/W1562283895","https://openalex.org/W1589711670","https://openalex.org/W1604594841","https://openalex.org/W1699931448","https://openalex.org/W1763084590","https://openalex.org/W1806862383","https://openalex.org/W1964647046","https://openalex.org/W1972814610","https://openalex.org/W1975653808","https://openalex.org/W1990727398","https://openalex.org/W1997037354","https://openalex.org/W1998081523","https://openalex.org/W2000118875","https://openalex.org/W2002328599","https://openalex.org/W2005335312","https://openalex.org/W2008600488","https://openalex.org/W2022226854","https://openalex.org/W2026455391","https://openalex.org/W2039654728","https://openalex.org/W2049209348","https://openalex.org/W2056385879","https://openalex.org/W2064508306","https://openalex.org/W2066725205","https://openalex.org/W2069547077","https://openalex.org/W2070863577","https://openalex.org/W2076263584","https://openalex.org/W2086162968","https://openalex.org/W2110784116","https://openalex.org/W2115826265","https://openalex.org/W2117111784","https://openalex.org/W2117541535","https://openalex.org/W2135734455","https://openalex.org/W2154949534","https://openalex.org/W2156495052","https://openalex.org/W2162583406","https://openalex.org/W2185277039","https://openalex.org/W2319549361","https://openalex.org/W2762861458","https://openalex.org/W2912251669","https://openalex.org/W3101545656","https://openalex.org/W3145062246","https://openalex.org/W4232979902","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2017318974","https://openalex.org/W1998380256","https://openalex.org/W111608424","https://openalex.org/W2136363749","https://openalex.org/W3120475523","https://openalex.org/W4249711300","https://openalex.org/W2077359248","https://openalex.org/W2092901979","https://openalex.org/W2951100677","https://openalex.org/W1965367600"],"abstract_inverted_index":{"Systems":[0],"of":[1,3,42,47,55,122,129,138,147],"equations":[2,57,102,124],"the":[4,18,25,52,119,150,153,156,164],"form":[5],"Xi":[6,20],"=":[7],"\u03d5i(X1,...,Xn),":[8],"for":[9,36,60,100],"1":[10],"\u2a7d":[11,13],"i":[12],"n":[14],",":[15],"in":[16],"which":[17],"unknowns":[19],"are":[21,34],"formal":[22,148],"languages,":[23,152,155,158,166],"and":[24,32,65,76,108],"right-hand":[26],"sides":[27],"\u03d5i":[28],"may":[29,58],"contain":[30],"concatenation":[31],"union,":[33],"known":[35],"representing":[37],"context-free":[38,157,165],"grammars.":[39],"If,":[40],"instead":[41],"union":[43,64],"only,":[44],"another":[45],"set":[46,128],"Boolean":[48,84,104,130,139],"operations":[49,85,140],"is":[50,133],"used,":[51],"expressive":[53,120],"power":[54,121],"such":[56,123],"change:":[59],"example,":[61],"using":[62,82],"both":[63],"intersection":[66],"leads":[67],"to":[68,90,143],"conjunctive":[69,154],"grammars":[70],"[A.":[71,96],"Okhotin,":[72,97],"J.":[73],"Automata,":[74,106],"Languages":[75,107],"Combinatorics":[77],"6":[78],"(2001)":[79],"519\u2013535],":[80],"whereas":[81],"all":[83,87],"allows":[86],"recursive":[88,151],"sets":[89,137],"be":[91],"expressed":[92],"by":[93],"unique":[94],"solutions":[95],"Decision":[98],"problems":[99],"language":[101],"with":[103,125,163],"operations,":[105],"Programming,":[109],"ICALP":[110],"2003,":[111],"Eindhoven,":[112],"The":[113],"Netherlands,":[114],"239\u2013251].":[115],"This":[116],"paper":[117],"investigates":[118],"any":[126],"possible":[127],"operations.":[131],"It":[132],"determined":[134],"that":[135],"different":[136],"give":[141],"rise":[142],"exactly":[144],"seven":[145],"families":[146],"languages:":[149],"a":[159],"certain":[160],"family":[161],"incomparable":[162],"as":[167,169],"well":[168],"three":[170],"subregular":[171],"families.":[172]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
