{"id":"https://openalex.org/W1531234133","doi":"https://doi.org/10.1016/s0304-3975(98)00006-1","title":"Boolean operations, joins, and the extended low hierarchy","display_name":"Boolean operations, joins, and the extended low hierarchy","publication_year":1998,"publication_date":"1998-09-01","ids":{"openalex":"https://openalex.org/W1531234133","doi":"https://doi.org/10.1016/s0304-3975(98)00006-1","mag":"1531234133"},"language":"en","primary_location":{"id":"doi:10.1016/s0304-3975(98)00006-1","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0304-3975(98)00006-1","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/s0304-3975(98)00006-1","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088546793","display_name":"Lane A. Hemaspaandra","orcid":"https://orcid.org/0000-0003-0659-5204"},"institutions":[{"id":"https://openalex.org/I5388228","display_name":"University of Rochester","ror":"https://ror.org/022kthw22","country_code":"US","type":"education","lineage":["https://openalex.org/I5388228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lane A. Hemaspaandra","raw_affiliation_strings":["Department of Computer Science, University of Rochester, Rochester, NY 14627, USA","University of Rochester; Rochester, NY"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Rochester, Rochester, NY 14627, USA","institution_ids":["https://openalex.org/I5388228"]},{"raw_affiliation_string":"University of Rochester; Rochester, NY","institution_ids":["https://openalex.org/I5388228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044020537","display_name":"Zhigen Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhigen Jiang","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences, Beijing 100080, China","Chinese Academy of Sciences , Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences, Beijing 100080, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Chinese Academy of Sciences , Beijing, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050661976","display_name":"J\u00f6rg Rothe","orcid":"https://orcid.org/0000-0002-0589-3616"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"J\u00f6rg Rothe","raw_affiliation_strings":["Institut f\u00fcr Informatik, Friedrich-Schiller-Universit\u00e4t Jena, 07743 Jena, Germany","Friedrich Schiller University Jena , Jena , Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Friedrich-Schiller-Universit\u00e4t Jena, 07743 Jena, Germany","institution_ids":["https://openalex.org/I76198965"]},{"raw_affiliation_string":"Friedrich Schiller University Jena , Jena , Germany","institution_ids":["https://openalex.org/I76198965"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088236477","display_name":"Osamu Watanabe","orcid":"https://orcid.org/0000-0003-0284-7566"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Osamu Watanabe","raw_affiliation_strings":["Department of Computer Science, Tokyo Institute of Technology, Tokyo 152, Japan","[Tokyo Institute of Technology, Tokyo, JAPAN]"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Tokyo Institute of Technology, Tokyo 152, Japan","institution_ids":["https://openalex.org/I114531698"]},{"raw_affiliation_string":"[Tokyo Institute of Technology, Tokyo, JAPAN]","institution_ids":["https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5050661976"],"corresponding_institution_ids":["https://openalex.org/I76198965"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":1.0171,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.73188343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"205","issue":"1-2","first_page":"317","last_page":"327"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9972000122070312,"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":0.9951000213623047,"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/hierarchy","display_name":"Hierarchy","score":0.8486369848251343},{"id":"https://openalex.org/keywords/join","display_name":"Join (topology)","score":0.8431655764579773},{"id":"https://openalex.org/keywords/joins","display_name":"Joins","score":0.785036563873291},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.6195290684700012},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5879812240600586},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47817426919937134},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40867772698402405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3367956876754761},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3177048861980438}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.8486369848251343},{"id":"https://openalex.org/C2776124973","wikidata":"https://www.wikidata.org/wiki/Q3183033","display_name":"Join (topology)","level":2,"score":0.8431655764579773},{"id":"https://openalex.org/C2778692605","wikidata":"https://www.wikidata.org/wiki/Q4041866","display_name":"Joins","level":2,"score":0.785036563873291},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6195290684700012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5879812240600586},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47817426919937134},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40867772698402405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3367956876754761},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3177048861980438},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0304-3975(98)00006-1","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0304-3975(98)00006-1","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:t2r2.star.titech.ac.jp:50030807","is_oa":false,"landing_page_url":"http://t2r2.star.titech.ac.jp/cgi-bin/publicationinfo.cgi?q_publication_content_number=CTT100555864","pdf_url":null,"source":{"id":"https://openalex.org/S4377196385","display_name":"Tokyo Tech Research Repository (Tokyo Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114531698","host_organization_name":"Tokyo Institute of Technology","host_organization_lineage":["https://openalex.org/I114531698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1016/s0304-3975(98)00006-1","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0304-3975(98)00006-1","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W639289183","https://openalex.org/W1505859165","https://openalex.org/W1964176779","https://openalex.org/W1970089350","https://openalex.org/W1982717290","https://openalex.org/W1986637231","https://openalex.org/W1999384241","https://openalex.org/W1999609654","https://openalex.org/W2007464118","https://openalex.org/W2011042573","https://openalex.org/W2016666233","https://openalex.org/W2018099718","https://openalex.org/W2021084256","https://openalex.org/W2033908054","https://openalex.org/W2044558965","https://openalex.org/W2050774914","https://openalex.org/W2062856555","https://openalex.org/W2065251436","https://openalex.org/W2067811682","https://openalex.org/W2092130624","https://openalex.org/W2140152225","https://openalex.org/W2144669277","https://openalex.org/W2157273288","https://openalex.org/W2165293955","https://openalex.org/W2175296692","https://openalex.org/W6630278492","https://openalex.org/W6642755269","https://openalex.org/W6651922783","https://openalex.org/W6683459261","https://openalex.org/W6911322511"],"related_works":["https://openalex.org/W2393491644","https://openalex.org/W4206577045","https://openalex.org/W650102067","https://openalex.org/W3086237447","https://openalex.org/W2740404111","https://openalex.org/W1550806730","https://openalex.org/W1496672428","https://openalex.org/W2589740103","https://openalex.org/W1966967794","https://openalex.org/W1501284171"],"abstract_inverted_index":{"We":[0,88],"prove":[1,97],"that":[2,30,77,98],"the":[3,16,23,34,38,56,68,78,91,112],"join":[4,45,57,69],"of":[5,15,22,37,53,94],"two":[6],"sets":[7,29],"may":[8,126],"actually":[9],"fall":[10],"into":[11],"a":[12,64,85],"lower":[13,60,72,118],"level":[14,36],"extended":[17,39,54,79],"low":[18,40,80],"hierarchy":[19,81],"than":[20],"either":[21],"sets.":[24],"In":[25],"particular,":[26],"there":[27],"exist":[28],"are":[31],"not":[32,71,101],"in":[33,47,51,63,133],"second":[35],"hierarchy,":[41],"EL2,":[42],"yet":[43],"their":[44],"is":[46,82,100],"EL2.":[48],"That":[49],"is,":[50],"terms":[52],"lowness,":[55],"operator":[58],"can":[59],"complexity.":[61],"Since":[62],"strong":[65],"intuitive":[66],"sense":[67],"does":[70],"complexity,":[73],"our":[74],"result":[75,132],"suggests":[76],"unnatural":[83],"as":[84,129],"complexity":[86],"measure.":[87],"also":[89],"study":[90],"closure":[92],"properties":[93],"EL2":[95,99,117],"and":[96],"closed":[102],"under":[103],"certain":[104,121],"Boolean":[105],"operations.":[106],"To":[107],"this":[108],"end,":[109],"we":[110],"establish":[111],"first":[113],"known":[114],"(and":[115],"optimal)":[116],"bounds":[119],"for":[120],"notions":[122],"generalizing":[123],"P-selectivity,":[124],"which":[125],"be":[127],"regarded":[128],"an":[130],"interesting":[131],"its":[134],"own":[135],"right.":[136]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}