{"id":"https://openalex.org/W1533036729","doi":"https://doi.org/10.1007/s00224-013-9515-7","title":"Quotient Complexity of Closed Languages","display_name":"Quotient Complexity of Closed Languages","publication_year":2013,"publication_date":"2013-11-18","ids":{"openalex":"https://openalex.org/W1533036729","doi":"https://doi.org/10.1007/s00224-013-9515-7","mag":"1533036729"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-013-9515-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-013-9515-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","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/A5016883956","display_name":"Janusz Brzozowski","orcid":"https://orcid.org/0000-0003-3390-2767"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Janusz Brzozowski","raw_affiliation_strings":["David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1","David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada N2L 3G1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada N2L 3G1","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012840795","display_name":"Galina Jir\u00e1skov\u00e1","orcid":"https://orcid.org/0000-0001-9817-8197"},"institutions":[{"id":"https://openalex.org/I207624831","display_name":"Slovak Academy of Sciences","ror":"https://ror.org/03h7qq074","country_code":"SK","type":"government","lineage":["https://openalex.org/I207624831"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Galina Jir\u00e1skov\u00e1","raw_affiliation_strings":["Mathematical Institute, Slovak Academy of Sciences, Gre\u0161\u00e1kova 6, 040 01, Ko\u0161ice, Slovakia","Mathematical Institute, Slovak Academy of Sciences, Ko\u0161ice, Slovakia 040 01#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Slovak Academy of Sciences, Gre\u0161\u00e1kova 6, 040 01, Ko\u0161ice, Slovakia","institution_ids":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]},{"raw_affiliation_string":"Mathematical Institute, Slovak Academy of Sciences, Ko\u0161ice, Slovakia 040 01#TAB#","institution_ids":["https://openalex.org/I207624831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049095702","display_name":"Chenglong Zou","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Chenglong Zou","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T 1Z4","Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z4#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T 1Z4","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z4#TAB#","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.9797,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.90477246,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"54","issue":"2","first_page":"277","last_page":"292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9912999868392944,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9864000082015991,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/suffix","display_name":"Suffix","score":0.7626007795333862},{"id":"https://openalex.org/keywords/concatenation","display_name":"Concatenation (mathematics)","score":0.6925339698791504},{"id":"https://openalex.org/keywords/prefix","display_name":"Prefix","score":0.6667453646659851},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.6321351528167725},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.6233723759651184},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6095418334007263},{"id":"https://openalex.org/keywords/subsequence","display_name":"Subsequence","score":0.5914450883865356},{"id":"https://openalex.org/keywords/formal-language","display_name":"Formal language","score":0.5188987851142883},{"id":"https://openalex.org/keywords/abstract-family-of-languages","display_name":"Abstract family of languages","score":0.4959281384944916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48319211602211},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.4805091619491577},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4486267864704132},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43872272968292236},{"id":"https://openalex.org/keywords/transitive-closure","display_name":"Transitive closure","score":0.4259960353374481},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.42120489478111267},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37283921241760254},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.22464364767074585},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1829429566860199},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.17226168513298035},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.13670411705970764},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07858511805534363}],"concepts":[{"id":"https://openalex.org/C2779804580","wikidata":"https://www.wikidata.org/wiki/Q102047","display_name":"Suffix","level":2,"score":0.7626007795333862},{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.6925339698791504},{"id":"https://openalex.org/C141603448","wikidata":"https://www.wikidata.org/wiki/Q134830","display_name":"Prefix","level":2,"score":0.6667453646659851},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6321351528167725},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.6233723759651184},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6095418334007263},{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.5914450883865356},{"id":"https://openalex.org/C146072743","wikidata":"https://www.wikidata.org/wiki/Q192161","display_name":"Formal language","level":2,"score":0.5188987851142883},{"id":"https://openalex.org/C199163288","wikidata":"https://www.wikidata.org/wiki/Q3065587","display_name":"Abstract family of languages","level":5,"score":0.4959281384944916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48319211602211},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4805091619491577},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4486267864704132},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43872272968292236},{"id":"https://openalex.org/C128896722","wikidata":"https://www.wikidata.org/wiki/Q1501387","display_name":"Transitive closure","level":2,"score":0.4259960353374481},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.42120489478111267},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37283921241760254},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.22464364767074585},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1829429566860199},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.17226168513298035},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.13670411705970764},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07858511805534363},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C11164408","wikidata":"https://www.wikidata.org/wiki/Q18657800","display_name":"Second-generation programming language","level":4,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00224-013-9515-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-013-9515-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.730.7728","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.730.7728","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://maveric.uwaterloo.ca/reports/2010_CSR_Brzozowski.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.743.1156","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.743.1156","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0912.1034.pdf","raw_type":"text"},{"id":"pmh:oai:uwspace.uwaterloo.ca:10012/12511","is_oa":false,"landing_page_url":"http://hdl.handle.net/10012/12511","pdf_url":null,"source":{"id":"https://openalex.org/S4306401661","display_name":"UWSpace (University of Waterloo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I151746483","host_organization_name":"University of Waterloo","host_organization_lineage":["https://openalex.org/I151746483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W560293","https://openalex.org/W32599491","https://openalex.org/W82038809","https://openalex.org/W95660754","https://openalex.org/W127832380","https://openalex.org/W392721968","https://openalex.org/W1503154721","https://openalex.org/W1525645762","https://openalex.org/W1532642937","https://openalex.org/W1761787697","https://openalex.org/W1988560957","https://openalex.org/W2005776781","https://openalex.org/W2006629323","https://openalex.org/W2015009579","https://openalex.org/W2019791627","https://openalex.org/W2025521996","https://openalex.org/W2063145078","https://openalex.org/W2067692482","https://openalex.org/W2068318378","https://openalex.org/W2094518278","https://openalex.org/W2106875872","https://openalex.org/W2108842989","https://openalex.org/W2109036808","https://openalex.org/W2151646486","https://openalex.org/W2156429182","https://openalex.org/W2158538677","https://openalex.org/W2408564624","https://openalex.org/W2498187449","https://openalex.org/W2570765932","https://openalex.org/W2676854164","https://openalex.org/W2913376930","https://openalex.org/W4248122200","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2017318974","https://openalex.org/W1998380256","https://openalex.org/W2240836793","https://openalex.org/W1540583425","https://openalex.org/W4376863261","https://openalex.org/W111608424","https://openalex.org/W4249711300","https://openalex.org/W4384942687","https://openalex.org/W430776923","https://openalex.org/W2507842156"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
