{"id":"https://openalex.org/W2949744367","doi":"https://doi.org/10.2168/lmcs-1(3:4)2005","title":"Modularizing the Elimination of r=0 in Kleene Algebra","display_name":"Modularizing the Elimination of r=0 in Kleene Algebra","publication_year":2005,"publication_date":"2005-12-21","ids":{"openalex":"https://openalex.org/W2949744367","doi":"https://doi.org/10.2168/lmcs-1(3:4)2005","mag":"2949744367"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-1(3:4)2005","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-1(3:4)2005","pdf_url":"https://lmcs.episciences.org/2264/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/2264/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Christopher Hardin","orcid":null},"institutions":[{"id":"https://openalex.org/I202524275","display_name":"Smith College","ror":"https://ror.org/0497crr92","country_code":"US","type":"education","lineage":["https://openalex.org/I202524275"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Christopher Hardin","raw_affiliation_strings":["Department of Mathematics, Smith College, Northampton, Massachusetts 01063, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Smith College, Northampton, Massachusetts 01063, USA","institution_ids":["https://openalex.org/I202524275"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I202524275"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.38281513,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"Volume 1, Issue 3","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.3190000057220459,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.3190000057220459,"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/T12504","display_name":"Mathematics and Applications","score":0.07530000060796738,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.06700000166893005,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kleene-algebra","display_name":"Kleene algebra","score":0.9031999707221985},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.828000009059906},{"id":"https://openalex.org/keywords/kleenes-recursion-theorem","display_name":"Kleene's recursion theorem","score":0.7921000123023987},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5558000206947327},{"id":"https://openalex.org/keywords/universal-algebra","display_name":"Universal algebra","score":0.5228000283241272},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.49959999322891235}],"concepts":[{"id":"https://openalex.org/C206470798","wikidata":"https://www.wikidata.org/wiki/Q2634506","display_name":"Kleene algebra","level":2,"score":0.9031999707221985},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.828000009059906},{"id":"https://openalex.org/C123260079","wikidata":"https://www.wikidata.org/wiki/Q1933521","display_name":"Kleene's recursion theorem","level":2,"score":0.7921000123023987},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5558000206947327},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.5228000283241272},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.49959999322891235},{"id":"https://openalex.org/C152076505","wikidata":"https://www.wikidata.org/wiki/Q1126540","display_name":"French horn","level":2,"score":0.4925999939441681},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46380001306533813},{"id":"https://openalex.org/C189790780","wikidata":"https://www.wikidata.org/wiki/Q933932","display_name":"Horn clause","level":3,"score":0.4530999958515167},{"id":"https://openalex.org/C154564781","wikidata":"https://www.wikidata.org/wiki/Q5384236","display_name":"Equational logic","level":3,"score":0.3499000072479248},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34689998626708984},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3163999915122986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28369998931884766},{"id":"https://openalex.org/C170517529","wikidata":"https://www.wikidata.org/wiki/Q21998744","display_name":"Term algebra","level":5,"score":0.2651999890804291},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.2621999979019165}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2168/lmcs-1(3:4)2005","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-1(3:4)2005","pdf_url":"https://lmcs.episciences.org/2264/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:cs/0511097","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0511097","pdf_url":"https://arxiv.org/pdf/cs/0511097","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},{"id":"pmh:oai:doaj.org/article:6b38083ee02446cd9a0dc7380a97beb6","is_oa":true,"landing_page_url":"https://doaj.org/article/6b38083ee02446cd9a0dc7380a97beb6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 1, Issue 3 (2005)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-1(3:4)2005","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-1(3:4)2005","pdf_url":"https://lmcs.episciences.org/2264/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4524359699","display_name":null,"funder_award_id":"N00014-01-1-0968","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4568523763","display_name":"Kleene Algebra","funder_award_id":"0105586","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2949744367.pdf","grobid_xml":"https://content.openalex.org/works/W2949744367.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1489273657","https://openalex.org/W1493510080","https://openalex.org/W1566548834","https://openalex.org/W1574223981","https://openalex.org/W1755036513","https://openalex.org/W1998368317","https://openalex.org/W2010626618","https://openalex.org/W2117065635","https://openalex.org/W2142072439"],"related_works":[],"abstract_inverted_index":{"Given":[0],"a":[1],"universal":[2,61],"Horn":[3,35,62],"formula":[4,36],"of":[5,10,43,45,54,70,83,98],"Kleene":[6,55],"algebra":[7,56],"with":[8],"hypotheses":[9,69,94,97],"the":[11,34,51,60,71,81,99],"form":[12,72,100],"r":[13,73,101],"=":[14,74,102],"0,":[15],"it":[16],"is":[17,28,37,40,48,57,64],"already":[18],"known":[19],"that":[20,68],"we":[21],"can":[22,76],"efficiently":[23],"construct":[24],"an":[25,41],"equation":[26],"which":[27,47],"valid":[29],"if":[30,33],"and":[31],"only":[32],"valid.":[38],"This":[39,86],"example":[42],"<i>elimination":[44],"hypotheses</i>,":[46],"useful":[49],"because":[50],"equational":[52],"theory":[53,63],"decidable":[58],"while":[59],"not.":[65],"We":[66],"show":[67],"0":[75],"still":[77],"be":[78],"eliminated":[79],"in":[80],"presence":[82],"other":[84],"hypotheses.":[85],"lets":[87],"us":[88],"extend":[89],"any":[90],"technique":[91],"for":[92],"eliminating":[93],"to":[95],"include":[96],"0.":[103]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2019-06-27T00:00:00"}