{"id":"https://openalex.org/W2395088789","doi":"https://doi.org/10.2168/lmcs-11(3:9)2015","title":"Quantified Constraints and Containment Problems","display_name":"Quantified Constraints and Containment Problems","publication_year":2015,"publication_date":"2015-09-11","ids":{"openalex":"https://openalex.org/W2395088789","doi":"https://doi.org/10.2168/lmcs-11(3:9)2015","mag":"2395088789"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-11(3:9)2015","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-11(3:9)2015","pdf_url":"https://lmcs.episciences.org/1585/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/1585/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013230954","display_name":"Barnaby Martin","orcid":"https://orcid.org/0000-0002-4642-8614"},"institutions":[{"id":"https://openalex.org/I4210127577","display_name":"Middlesex University","ror":"https://ror.org/030ypay32","country_code":"MT","type":"education","lineage":["https://openalex.org/I4210127577"]},{"id":"https://openalex.org/I60488453","display_name":"Middlesex University","ror":"https://ror.org/01rv4p989","country_code":"GB","type":"education","lineage":["https://openalex.org/I60488453"]}],"countries":["GB","MT"],"is_corresponding":true,"raw_author_name":"Barnaby D. Martin","raw_affiliation_strings":["Science and Technology, Middlesex University, The Burroughs, Hendon, London NW4 4BT, U.K"],"affiliations":[{"raw_affiliation_string":"Science and Technology, Middlesex University, The Burroughs, Hendon, London NW4 4BT, U.K","institution_ids":["https://openalex.org/I60488453","https://openalex.org/I4210127577"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Hubie Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I110594554","display_name":"Ikerbasque","ror":"https://ror.org/01cc3fy72","country_code":"ES","type":"other","lineage":["https://openalex.org/I110594554"]},{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Hubie Chen","raw_affiliation_strings":["Basque Foundation for Science, E-48011 Bilbao, Spain","Departamento LSI, Facultad de Informtica, Universidad del Pas Vasco, E-20018 San Sebastin, Spain and IKERBASQUE,"],"affiliations":[{"raw_affiliation_string":"Basque Foundation for Science, E-48011 Bilbao, Spain","institution_ids":["https://openalex.org/I110594554"]},{"raw_affiliation_string":"Departamento LSI, Facultad de Informtica, Universidad del Pas Vasco, E-20018 San Sebastin, Spain and IKERBASQUE,","institution_ids":["https://openalex.org/I169108374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044720498","display_name":"Florent Madelaine","orcid":"https://orcid.org/0000-0002-8528-7105"},"institutions":[{"id":"https://openalex.org/I4210103002","display_name":"University of Clermont Auvergne","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210103002"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Florent R. Madelaine","raw_affiliation_strings":["Clermont Universit, Universit d'Auvergne, LIMOS, BP 10448, F-63000 Clermont-Ferrand, France"],"affiliations":[{"raw_affiliation_string":"Clermont Universit, Universit d'Auvergne, LIMOS, BP 10448, F-63000 Clermont-Ferrand, France","institution_ids":["https://openalex.org/I4210103002"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013230954"],"corresponding_institution_ids":["https://openalex.org/I4210127577","https://openalex.org/I60488453"],"apc_list":null,"apc_paid":null,"fwci":0.3638,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.69252008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"Volume 11, 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/T10374","display_name":"Advanced Graph Theory Research","score":0.4074999988079071,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.4074999988079071,"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/T10142","display_name":"Formal Methods in Verification","score":0.1860000044107437,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.13989999890327454,"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/homomorphism","display_name":"Homomorphism","score":0.7979073524475098},{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.7878587245941162},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7070921063423157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6472190022468567},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5941884517669678},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.48727381229400635},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36954614520072937},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25360965728759766},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0717805027961731}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.7979073524475098},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.7878587245941162},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7070921063423157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6472190022468567},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5941884517669678},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.48727381229400635},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36954614520072937},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25360965728759766},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0717805027961731},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2168/lmcs-11(3:9)2015","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-11(3:9)2015","pdf_url":"https://lmcs.episciences.org/1585/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:doaj.org/article:bcc2978e80334da59593dc95b1a12565","is_oa":true,"landing_page_url":"https://doaj.org/article/bcc2978e80334da59593dc95b1a12565","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 11, Issue 3 (2015)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-11(3:9)2015","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-11(3:9)2015","pdf_url":"https://lmcs.episciences.org/1585/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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.75}],"awards":[{"id":"https://openalex.org/G6739313371","display_name":null,"funder_award_id":"EP/L005654/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7341063109","display_name":"Infinite-domain Constraint Satisfaction Problems","funder_award_id":"EP/L005654/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2395088789.pdf","grobid_xml":"https://content.openalex.org/works/W2395088789.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1549008998","https://openalex.org/W1550394161","https://openalex.org/W1971626643","https://openalex.org/W1984074081","https://openalex.org/W1985274317","https://openalex.org/W1997649256","https://openalex.org/W2051474359","https://openalex.org/W2070051236","https://openalex.org/W2076946745","https://openalex.org/W2077575555","https://openalex.org/W2150339067","https://openalex.org/W2171491461","https://openalex.org/W2949624345"],"related_works":["https://openalex.org/W3015672237","https://openalex.org/W4308159138","https://openalex.org/W238609530","https://openalex.org/W4256653909","https://openalex.org/W1979798674","https://openalex.org/W4327811209","https://openalex.org/W3169947911","https://openalex.org/W2784745440","https://openalex.org/W1998601876","https://openalex.org/W1510423293"],"abstract_inverted_index":{"The":[0,143],"quantified":[1],"constraint":[2],"satisfaction":[3],"problem":[4,8,156,209,259],"$\\mathrm{QCSP}(\\mathcal{A})$":[5],"is":[6,25,54,70,86,125,139,190,217,240,248,269,285,302,317],"the":[7,20,39,107,132,136,149,153,165,207,257,272,276,290,296,300,311,323],"to":[9,38,58,92,110,118,128,169,172,196],"decide":[10],"whether":[11,236],"a":[12,44,87,113,176,183,191,280,319],"positive":[13,74,211,228,261,265],"Horn":[14,75,212,266],"sentence,":[15],"involving":[16],"nothing":[17],"more":[18],"than":[19],"two":[21,34,222],"quantifiers":[22],"and":[23,51,56,225],"conjunction,":[24],"true":[26,77,81,241],"on":[27,47,78,82],"some":[28,250,286],"fixed":[29,184],"structure":[30],"$\\mathcal{A}$.":[31],"We":[32,63,120,162],"study":[33],"containment":[35,130,155],"problems":[36],"related":[37],"QCSP.":[40,298],"Firstly,":[41],"we":[42,204,230,254,278,313],"give":[43,231],"combinatorial":[45],"condition":[46,124],"finite":[48],"structures":[49,179,244],"$\\mathcal{A}$":[50,79,180],"$\\mathcal{B}$":[52,197],"that":[53,65,69,105,122,138,188,206,234,256,284,294,315],"necessary":[55,127],"sufficient":[57],"render":[59],"$\\mathrm{QCSP}(\\mathcal{A})":[60,66],"\\subseteq":[61,67,141],"\\mathrm{QCSP}(\\mathcal{B})$.":[62],"prove":[64,205],"\\mathrm{QCSP}(\\mathcal{B})$,":[68],"all":[71,243],"sentences":[72,223],"of":[73,103,131,135,146,178,214,227,275,282,292,325],"logic":[76,216,263],"are":[80],"$\\mathcal{B}$,":[83,185],"iff":[84],"there":[85,111,189],"surjective":[88,114,192],"homomorphism":[89,115,193],"from":[90,116,194],"$\\mathcal{A}^{|A|^{|B|}}$":[91],"$\\mathcal{B}$.":[93,119],"This":[94],"can":[95],"be":[96,170],"seen":[97],"as":[98,304,306],"improving":[99],"an":[100,232],"old":[101],"result":[102,247],"Keisler":[104],"shows":[106],"former":[108],"equivalent":[109],"being":[112],"$\\mathcal{A}^\\omega$":[117],"note":[121],"this":[123],"already":[126],"guarantee":[129],"$\\Pi_2$":[133],"restriction":[134],"QCSP,":[137],"$\\Pi_2$-$\\mathrm{CSP}(\\mathcal{A})":[140],"\\Pi_2$-$\\mathrm{CSP}(\\mathcal{B})$.":[142],"exponent's":[144,166],"bound":[145,167],"${|A|^{|B|}}$":[147],"places":[148],"decision":[150],"procedure":[151],"for":[152,210,260],"model":[154],"in":[157,242,249,322],"non-deterministic":[158],"double-exponential":[159],"time":[160],"complexity.":[161],"further":[163],"show":[164,255],"$|A|^{|B|}$":[168],"close":[171],"tight":[173],"by":[174],"giving":[175],"sequence":[177],"together":[181],"with":[182],"$|B|=2$,":[186],"such":[187],"$\\mathcal{A}^r$":[195],"only":[198],"when":[199],"$r":[200],"\\geq":[201],"|A|$.":[202],"Secondly,":[203],"entailment":[208,258],"fragment":[213],"first-order":[215,262],"decidable.":[218],"That":[219],"is,":[220],"given":[221],"$\\varphi$":[224],"$\\psi$":[226],"Horn,":[229],"algorithm":[233],"determines":[235],"$\\varphi":[237],"\\rightarrow":[238],"\\psi$":[239],"(models).":[245],"Our":[246],"sense":[251],"tight,":[252],"since":[253],"(i.e.":[264],"plus":[267],"disjunction)":[268],"undecidable.":[270],"In":[271],"final":[273],"part":[274],"paper":[277],"ponder":[279],"notion":[281,321],"Q-core":[283,301],"canonical":[287],"representative":[288],"among":[289],"class":[291],"templates":[293],"engender":[295],"same":[297],"Although":[299],"not":[303],"well-behaved":[305],"its":[307],"better":[308],"known":[309],"cousin":[310],"core,":[312],"demonstrate":[314],"it":[316],"still":[318],"useful":[320],"realm":[324],"QCSP":[326],"complexity":[327],"classifications.":[328]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}