{"id":"https://openalex.org/W4306165440","doi":"https://doi.org/10.1017/s0960129522000329","title":"An algebraic representation of the fixed-point closure of *-continuous Kleene algebras \u2013 A categorical Chomsky\u2013Sch\u00fctzenberger theorem","display_name":"An algebraic representation of the fixed-point closure of *-continuous Kleene algebras \u2013 A categorical Chomsky\u2013Sch\u00fctzenberger theorem","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W4306165440","doi":"https://doi.org/10.1017/s0960129522000329"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129522000329","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129522000329","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B423ED951CD154761D1CCAE96A99BC4F/S0960129522000329a.pdf/div-class-title-an-algebraic-representation-of-the-fixed-point-closure-of-continuous-kleene-algebras-a-categorical-chomsky-schutzenberger-theorem-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B423ED951CD154761D1CCAE96A99BC4F/S0960129522000329a.pdf/div-class-title-an-algebraic-representation-of-the-fixed-point-closure-of-continuous-kleene-algebras-a-categorical-chomsky-schutzenberger-theorem-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023391589","display_name":"Hans Lei\u00df","orcid":"https://orcid.org/0000-0002-4162-2258"},"institutions":[{"id":"https://openalex.org/I4210088543","display_name":"Institut f\u00fcr Informationsverarbeitung","ror":"https://ror.org/0047j9t38","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210088543"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Hans Lei\u00df","raw_affiliation_strings":["Centrum f\u00fcr Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany\u2020","Centrum f\u00fcr Informations-und Sprachverarbeitung, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4162-2258","affiliations":[{"raw_affiliation_string":"Centrum f\u00fcr Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany\u2020","institution_ids":["https://openalex.org/I4210088543","https://openalex.org/I8204097"]},{"raw_affiliation_string":"Centrum f\u00fcr Informations-und Sprachverarbeitung, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I4210088543","https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023391589"],"corresponding_institution_ids":["https://openalex.org/I4210088543","https://openalex.org/I8204097"],"apc_list":null,"apc_paid":null,"fwci":0.1522,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51562614,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"32","issue":"6","first_page":"685","last_page":"728"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9961000084877014,"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/T10142","display_name":"Formal Methods in Verification","score":0.9958999752998352,"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/mathematics","display_name":"Mathematics","score":0.7422343492507935},{"id":"https://openalex.org/keywords/free-product","display_name":"Free product","score":0.558179497718811},{"id":"https://openalex.org/keywords/centralizer-and-normalizer","display_name":"Centralizer and normalizer","score":0.5319236516952515},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5257516503334045},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5148579478263855},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5088258385658264},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.46112316846847534},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.4534672498703003},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4229188859462738},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4212574362754822},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40680307149887085},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3525112271308899},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.283103883266449}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7422343492507935},{"id":"https://openalex.org/C47527751","wikidata":"https://www.wikidata.org/wiki/Q1454165","display_name":"Free product","level":3,"score":0.558179497718811},{"id":"https://openalex.org/C75174853","wikidata":"https://www.wikidata.org/wiki/Q190629","display_name":"Centralizer and normalizer","level":2,"score":0.5319236516952515},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5257516503334045},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5148579478263855},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5088258385658264},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.46112316846847534},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4534672498703003},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4229188859462738},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4212574362754822},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40680307149887085},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3525112271308899},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.283103883266449},{"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/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0960129522000329","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129522000329","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B423ED951CD154761D1CCAE96A99BC4F/S0960129522000329a.pdf/div-class-title-an-algebraic-representation-of-the-fixed-point-closure-of-continuous-kleene-algebras-a-categorical-chomsky-schutzenberger-theorem-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:epub.ub.uni-muenchen.de:94854","is_oa":true,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bvb:19-epub-94854-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401845","display_name":"Open access LMU (Ludwid Maxmilian's Universitat Munchen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8204097","host_organization_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","host_organization_lineage":["https://openalex.org/I8204097"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1017/s0960129522000329","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129522000329","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B423ED951CD154761D1CCAE96A99BC4F/S0960129522000329a.pdf/div-class-title-an-algebraic-representation-of-the-fixed-point-closure-of-continuous-kleene-algebras-a-categorical-chomsky-schutzenberger-theorem-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310145","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4306165440.pdf","grobid_xml":"https://content.openalex.org/works/W4306165440.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1489273657","https://openalex.org/W1494333725","https://openalex.org/W1522144493","https://openalex.org/W1527487696","https://openalex.org/W1570949334","https://openalex.org/W1597349423","https://openalex.org/W1635972851","https://openalex.org/W1890888469","https://openalex.org/W2026655482","https://openalex.org/W2078567245","https://openalex.org/W2111229114","https://openalex.org/W2120713972","https://openalex.org/W2163152086","https://openalex.org/W2546526558","https://openalex.org/W2616790502","https://openalex.org/W2894599866","https://openalex.org/W2894659279"],"related_works":["https://openalex.org/W2348675898","https://openalex.org/W2977487684","https://openalex.org/W2017756151","https://openalex.org/W1945927862","https://openalex.org/W2139874420","https://openalex.org/W2105904493","https://openalex.org/W2155037452","https://openalex.org/W2801448390","https://openalex.org/W4312623806","https://openalex.org/W2963078304"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"family":[2,31],"${\\mathcal{R}}":[3,88,104,138,197],"X^*$":[4,33],"of":[5,8,23,34,37,43,74,87,96,103,111,119,122,132,137,146,154,162,196,214,223,228],"regular":[6,113,188],"subsets":[7,36],"the":[9,20,30,40,72,84,112,130,135,144,194,211,221,226],"free":[10],"monoid":[11],"$X^*$":[12,38],"generated":[13],"by":[14,187],"a":[15,24,44,57,77,100,109,159],"finite":[16,183],"set":[17,145],"X":[18],"is":[19,39,54,71,127],"standard":[21,41],"example":[22,42],"${}^*$":[25,206],"-continuous":[26,46,79,207],"Kleene":[27,208],"algebra.":[28],"Likewise,":[29],"${\\mathcal{C}}":[32,69,97],"context-free":[35,180],"$\\mu$":[45,62,78],"Chomsky":[47,80,163],"algebra,":[48,81],"i.e.":[49,143],"an":[50,93,116],"idempotent":[51],"semiring":[52],"that":[53,149],"closed":[55],"under":[56],"well-behaved":[58],"least":[59],"fixed-point":[60,85,212],"operator":[61],".":[63,90,156,201,232],"For":[64],"arbitrary":[65],"monoids":[66],"M":[67],",":[68,108,142,172],"M$":[70,89,98,105,139,186,198],"closure":[73,86,213],"${\\mathcal{R}}M$":[75],"as":[76,220],"more":[82],"briefly,":[83],"We":[91],"provide":[92],"algebraic":[94],"representation":[95],"in":[99,134,193,225],"suitable":[101],"product":[102,136,195,227],"with":[106,140,151,230],"$C_2'$":[107,133,141,155,200,224,231],"quotient":[110],"sets":[114,184],"over":[115,182,190],"alphabet":[117],"$\\Delta_2$":[118],"two":[120],"pairs":[121],"bracket":[123],"symbols.":[124],"Namely,":[125],"${\\mathcal{C}}M$":[126],"isomorphic":[128],"to":[129,177],"centralizer":[131,222],"those":[147],"elements":[148,153],"commute":[150],"all":[152,179],"This":[157],"generalizes":[158],"well-known":[160],"result":[161],"and":[164,169,174,199],"Sch\u00fctzenberger":[165],"(1963,":[166],"Computer":[167],"Programming":[168],"Formal":[170],"Systems":[171],"118\u2013161)":[173],"admits":[175],"us":[176],"denote":[178],"languages":[181],"$X\\subseteq":[185],"expressions":[189],"$X\\cup\\Delta_2$":[191],"interpreted":[192],"More":[202],"generally,":[203],"for":[204],"any":[205],"algebra":[209],"K":[210,215,229],"can":[216],"be":[217],"represented":[218],"algebraically":[219]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
